*For more information, please visit my.harvard.edu*.

Fall 2019 courses

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**Spring 2020**

**PHYSCI 3 - Electromagnetism, Circuits, Waves, Optics, and Imaging** (Louis Deslauriers, Roxanne Guenette)

T, TH: 9:00am - 10:15am | Course website*This course is an introduction to electromagnetism, digital information, waves, optics and sound. Topics covered include: electric and magnetic fields, electrical potential, circuits, simple digital circuits, wave propagation in various media, microscopy, sound and hearing. The course will draw upon a variety of applications to the biological sciences and will use real-world examples to illustrate many of the physical principles described. There are six laboratories. *

**PHYSCI 12A - Mechanics from an Analytic, Numerical and Experimental Perspective** (Efthimios Kaxiras, Camille Gomez-Laberge)

M, W, F: 9:00am - 10:15am | Course website*This is the first term of a two-semester introductory physical science and engineering course sequence. The focus is on quantitative scientific reasoning, with the first term's exploration framed in the context of basic mechanics. Students will gain competence in both analytic (using pencil, paper and single-variable calculus) and numerical (using computer modeling) approaches to modeling simple physical systems and for the analysis of experimental data. Topics include kinematics, linear and rotational motion, forces, energy, collisions, gravitation, simple fluids and a brief introduction to waves. Examples are drawn from across the physical sciences and engineering. The course is aimed at first year students who have an interest in pursuing a concentration in the sciences and/or engineering. The course structure includes lecture, discussion and laboratory components.*

**PHYSICS 15A - Introductory Mechanics and Relativity** (Julia Mundy, Keith Zengel, Carey Witkov)

T, TH: 12:00pm - 1:15pm | Course website*Newtonian mechanics and special relativity. Topics include vectors; kinematics in three dimensions; Newton's laws; force, work, power; conservative forces, potential energy; momentum, collisions; rotational motion, angular momentum, torque; static equilibrium, oscillations, simple harmonic motions; gravitation, planetary motion; fluids; special relativity. *

**PHYSICS 15B - Introductory Electromagnetism and Statistical Physics** (Cora Dvorkin, Amir Yacoby, Carey Witkov, Keith Zengel)

T, TH: 12:00pm - 1:15pm | Course website *Electricity and magnetism. Topics include electrostatics, electric currents, magnetic field, electromagnetic induction, Maxwell’s equations, electromagnetic radiation, magnetic fields in materials, and some basic notions in kinetic theory, entropy, temperature, and phase transition associated with electricity and magnetism. *

**PHYSICS 15C - Wave Phenomena** (Matthew Reece, Mara Prentiss)

M, W: 10:30am - 11:45am | Course website *Forced oscillation and resonance; coupled oscillators and normal modes; Fourier series; Electromagnetic waves, radiation, longitudinal oscillations, sound; traveling waves; signals, wave packets and group velocity; two- and three-dimensional waves; polarization; geometrical and physical optics; interference and diffraction. Optional topics: Water waves, holography, x-ray crystallography, solitons, music, quantum mechanics, and waves in the early universe. *

**PHYSICS 90R - Supervised Research** (David J. Morin)

Course website*Primarily for selected concentrators in Physics, or in Chemistry and Physics, who have obtained honor grades in Physics 15 and a number of intermediate-level courses. The student must be accepted by some member of the faculty doing research in the student's field of interest. The form of the research depends on the student's interest and experience, the nature of the particular field of physics, and facilities and support available. Students wishing to write a senior thesis can do so by arranging for a sponsor and enrolling in this course. *

**PHYSICS 91R - Supervised Reading Course for Undergraduates** (David J. Morin)

Course website *Open to selected concentrators in Physics, Chemistry and Physics, and other fields who wish to do supervised reading and studying of special topics in physics. Ordinarily such topics do not include those covered in a regular course of the Department. Honor grades in Physics 15 and a number of intermediate-level courses are ordinarily required. The student must be accepted by a member of the faculty.*

**PHYSICS 123 - Laboratory Electronics** (Tom Hayes, David Abrams)

option 1: T, TH: 1:30pm - 5:45pm

option 2: W, F: 1:30pm - 5:45pm

Course website*A lab-intensive introduction to electronic circuit design. Develops circuit intuition and debugging skills through daily hands-on lab exercises, each preceded by class discussion, with minimal use of mathematics and physics. Moves quickly from passive circuits, to discrete transistors, then concentrates on operational amplifiers, used to make a variety of circuits including integrators, oscillators, regulators, and filters. The digital half of the course treats analog-digital interfacing, emphasizes the use of microcontrollers and programmable logic devices (PLDs). *

**PHYSICS 125 - Widely Applied Physics** (David J. Morin)

W, F: 12:00pm - 1:15pm | Course website*Uses physics to analyze important technologies and real world systems. Stresses estimation and “back of the envelope” calculations, as are commonly used by research physicists when addressing new problems and analyzing national and international policy issues. New physical concepts are introduced as necessary. Example topics: energy production and storage (solar, nuclear, batteries), nuclear physics, power and weapons, airplanes, spy satellites, rockets, fluids, health effects of radiation, risk analysis, mechanical design and failure, communication, computation, global warming. Emphasis is on developing physical intuition and the ability to do order-of-magnitude calculations. *

**PHYSICS 129 - Energy Science** (Lene Hau)

T, TH: 1:30pm - 2:45pm | Course website*Non-fossil energy sources and energy storage are important for our future. We cover four main subjects to which students with a background in physics and physical chemistry could make paradigm changing contributions: photovoltaic cells, nuclear power, batteries, and photosynthesis. Fundamentals of electrodynamics, statistical/thermal physics, and quantum mechanics are taught as needed to give students an understanding of the topics covered.*

**PHYSICS 143A - Quantum Mechanics I** (Masahiro Morii)

T, TH: 10:30am - 11:45am | Course website*Introduction to nonrelativistic quantum mechanics: uncertainty relations; Schrödinger equation; Dirac notation; matrix mechanics; one-dimensional problems including particle in box, tunneling, and harmonic oscillator; angular momentum, hydrogen atom, spin, Pauli principle; and if time allows: time-independent perturbation theory; and scattering. *

**PHYSICS 153 - Electrodynamics** (Girma Hailu)

M, W: 12:00pm - 1:15pm | Course website*Aimed at advanced undergraduates. Emphasis on the properties and sources of the electromagnetic fields and on the wave aspects of the fields. Course starts with electrostatics and subsequently develops the Maxwell equations. Topics: electrostatics, dielectrics, magnetostatics, electrodynamics, radiation, wave propagation in various media, wave optics, diffraction and interference. A number of applications of electrodynamics and optics in modern physics are discussed. *

**PHYSICS 160 - Introduction to quantum information** (Mikhail Lukin)

M, W: 10:30am - 11:45am | Course website*Introduction to quantum information science, including quantum computation, communication and metrology. Emphasis on fundamental principles, experimental implementations and applications. Background and theoretical techniques will be introduced. *

**PHYSICS 175 - Laser Physics and Modern Optical Physics** (Markus Greiner)

W, F: 1:30pm - 2:45pm | Course website*Introduction to laser physics and modern optical physics aimed at advanced undergraduates. Review of electromagnetic theory and relevant aspects of quantum mechanics. Wave nature of light. Physics of basic optical elements. Propagation of focused beams, optical resonators, dielectric waveguides. Interaction of light with matter, introduction to quantum optics. Lasers. Physics of specific laser systems. Introduction to nonlinear optics. Modern applications. *

**PHYSICS 181 - Statistical Mechanics and Thermodynamics** (Matthew D. Schwartz)

T, TH: 12:00pm - 1:15pm | Course website*Introduction to thermal physics and statistical mechanics: basic concepts of thermodynamics (energy, heat, work, temperature, and entropy), classical and quantum ensembles and their origins, and distribution functions. Applications include the specific heat of solids, black body radiation; classical and quantum gases; magnetism; phase transitions; propagation of heat and sound.*

**PHYSICS 191 - Advanced Laboratory** (Isaac F. Silvera, Jenny Hoffman)

T, TH: 1:30pm - 5:45pm | Course website*Students carry out three experimental projects selected from those available representing condensed matter, atomic, nuclear, and particle physics. Included are pulsed nuclear magnetic resonance (with MRI), microwave spectroscopy, optical pumping, Raman scattering, scattering of laser light, nitrogen vacancies in diamond, neutron activation of radioactive isotopes, Compton scattering, relativistic mass of the electron, recoil free gamma-ray resonance, lifetime of the muon, studies of superfluid helium, positron annihilation, superconductivity, the quantum Hall effect, properties of semiconductors. The facilities of the laboratory include several computer controlled experiments as well as computers for analysis.*

**PHYSICS 201 - Data Analysis for Physicists** (Vinothan Manoharan)

M, W, F: 10:30am - 11:45am | Course website*This course covers what to do with experimental data after acquiring it. We will start with how to load, parse, filter, and visualize data using modern computational tools, then proceed to more advanced methods including Markov chain Monte Carlo and time-series analysis. Throughout, students will learn methods of statistical inference from both frequentist and Bayesian frameworks. Applications to particle physics, biophysics, condensed matter, applied physics, astrophysics, and more. *

**PHYSICS 210 - General Theory of Relativity** (Jacob Barandes)

M, W, F: 3:00pm - 4:15pm | Course website*An introduction to general relativity: the principle of equivalence, Riemannian geometry, Einstein's field equation, the Schwarzschild solution, the Newtonian limit, experimental tests, black holes. *

**PHYSICS 211AR - Topics in Cosmology and Particle Physics** (Lisa Randall)

W: 1:30pm - 4:15pm | Course website*This course will be about particle physics and cosmology, focusing on those aspects of cosmology most relevant to people studying particle model building and phenomenology. Topics will include inflation, dark matter, and dark energy. The course will be seminar style, with presentations by the lecturer and by students. The aim is to gear up for topics relevant to current research. *

**PHYSICS 211BR - Black Holes from A to Z** (Andrew Strominger)

W: 3:00pm - 5:45pm | Course website*A survey of a variety of issues in black hole physics. A central focus will be the deep 'information paradox' they present concerning the relations between general relativity, quantum mechanics and thermodynamics. Several expert guest speakers will cover more astrophysical, mathematical and historical aspects of black holes. Topics include: the information puzzle, the Bekenstein-Hawking entropy/area law, microstate counting, asymptotic symmetries, soft hair, holography and Kerr/CFT. *

**PHYSICS 211CR - Cosmology and Other Topics** (TBA)

T, TH: 10:30am - 11:45am | Course website*Standard cosmological model and inflation, scalar inflationary models, cosmological perturbation theory, brief introduction to quantum fields on cosmological backgrounds, interactions and in-in (Keldysh-Schwinger) perturbation theory, non-gaussianities, symmetries and cosmological Ward identities.*

**PHYSICS 216 - Mathematics of Modern Physics** (Arthur Jaffe)

T, TH: 10:30am - 11:45am | Course website*Introduction to functional analytic methods relevant for problems in quantum and statistical physics. Properties of linear transformations on Hilbert space. Generators of continuous groups and semigroups. Properties of Green's functions and matrices. Uniqueness and non-uniqueness of ground states and equilibrium states. Heat kernel methods. Index theory, invariants, and related algebraic structure. The KMS condition and its consequences. *

**PHYSICS 223 - Electronics for Scientists**: see PHYSICS 123

**PHYSICS 232 - Advanced Electromagnetism** (Subir Sachdev)

M, W, F: 3:00pm - 4:15pm | Course website*Maxwell's equations in macroscopic media, conservation laws, Green's functions, time-dependent solutions and radiation, scattering and diffraction, and gauge invariance. Time permitting: geometrical optics and caustics, negative refractive index materials and radiation from rapidly accelerating charges.*

**PHYSICS 247 - Laboratory Course in Contemporary Physics: **see PHYSICS 191

**PHYSICS 251B - Advanced Quantum Mechanics II** (Ashvin Vishwanath)

T, TH: 1:30pm - 2:45pm | Course website*Path integrals; relativistic quantum mechanics and quantum fields; identical particles; scattering theory; quantum information theory.*

**PHYSICS 253B - Quantum Field Theory II** (Daniel Jafferis)

W, F: 1:30pm - 2:45pm | Course website*A continuation of Physics 253a. Topics include: the renormalization group, implications of unitarity, Yang-Mills theories, spontaneous symmetry breaking, weak interactions, anomalies, and quantum chromodynamics. Additional advanced topics may be covered depending on time and interest. *

**PHYSICS 264 - Lie Algebras, Representations and Quantum Mechanics** (Howard Georgi)

T, TH: 3:00pm - 4:15pm | Course website*Lie algebras and their representations are indispensible tools in quantum mechanics. Starting from the operator treatment of angular momentum, this course explores some of the (many) useful approaches to this subject with applications in various areas of physics. *

**PHYSICS 268BR - Renormalization Group Methods in Condensed Matter Physics** (David R. Nelson)

M, W, F: 10:30am - 11:45am | Course website*Renormalization group ideas have had a major impact on condensed matter physics. We plan to develop and illustrate the theory by studying at least three of the following topics: (1) critical phenomena near four dimensions; (2) quantum critical points in Heisenberg spins; (3) flexural phonons in free-standing graphene; and (4) the fluid dynamics of the forced Navier-Stokes equations. *

**PHYSICS 287BR - The String Landscape and the String Swampland** (Xi Yin)

TH: 12:00pm - 2:45pm | Course website*A selection of topics from current areas of research on string theory. *

**PHYSICS 295B - Quantum Theory of Solids** (Eugene Demler)

M, W: 12:00pm - 1:15pm | Course website*This course presents theoretical description of solids focusing on the effects of interactions between electrons. Topics include Fermi liquid theory, dielectric response and RPA approximation, ferro and antiferromagnetism, RKKY interactions and Kondo effect, electron-phonon interactions and superconductivity *

**PHYSICS 296 - Mesoscale and Low Dimensional Devices** (Philip Kim)

W, F: 1:30pm - 2:45pm | Course website*Concepts of condensed matter physics are applied to the science and technology of beyond-CMOS devices, in particular, mesoscale, low-dimensional, and superconducting devices. Topics include: quantum dots/wires/wells and two-dimensional (2D) materials; optoelectronics with confined electrons; conductance quantization, Landauer-Buttiker formalism, and resonant tunneling; magneto oscillation; integer and fractional quantum Hall effects; Berry phase and topology in condensed matter physics; various Hall effects (anomalous, spin, valley, etc.); Weyl semimetal; topological insulator; spintronic devices and circuits; collective electron behaviors in low dimensions and applications; Cooper-pair boxes and superconducting quantum circuits.*

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**Fall 2019**

**PHYSCI 2 - Mechanics, Elasticity, Fluids, and Diffusion** (Gregory Kestin)

T, TH: 9:00am - 10:15am | Course website*An introduction to classical mechanics, with special emphasis on the motion of organisms in fluids. Topics covered include: kinematics, Newton's laws of motion, oscillations, elasticity, random walks, diffusion, and fluids. Examples and problem set questions will be drawn from the life sciences and medicine. *

**PHYSICS 12B - Electromagnetism and Statistical Physics from an Analytic, Numerical and Experimental Perspective** (Logan McCarty, Efthimios Kaxiras)

M, W, F: 9:00am - 10:15am | Course website*This is the second term of a two-semester introductory sequence that uses a combination of analytic and numerical methods to understand physical systems, to analyze experimental data, and to compare data to models. Topics include electrostatics and magnetostatics, electromagnetic fields, optics [all topics illustrated with applications to current technological and societal challenges], and an introduction to the physics of many-body systems and their aggregate properties such as entropy, temperature and pressure. The course is aimed at second year students who have an interest in pursuing a concentration in the sciences and/or engineering. The course structure includes lecture, discussion and laboratory components. *

**PHYSICS 15A - Introductory Mechanics and Relativity** (David J. Morin, Amir Yacoby, Carey Witkov, Keith Zengel)

T, TH: 12:00pm - 1:15pm | Course website*Newtonian mechanics and special relativity. Topics include vectors; kinematics in three dimensions; Newton's laws; force, work, power; conservative forces, potential energy; momentum, collisions; rotational motion, angular momentum, torque; static equilibrium, oscillations, simple harmonic motions; gravitation, planetary motion; fluids; special relativity. *

**PHYSICS 15B - Introductory Electromagnetism and Statistical Physics**

(Philip Kim, Robert Westervelt, Carey Witkov, Keith Zengel)

T, TH: 12:00pm - 1:15pm | Course website *Electricity and magnetism. Topics include electrostatics, electric currents, magnetic field, electromagnetic induction, Maxwell’s equations, electromagnetic radiation, magnetic fields in materials, and some basic notions in kinetic theory, entropy, temperature, and phase transition associated with electricity and magnetism. *

**PHYSICS 15C - Wave Phenomena** (Markus Greiner, Melissa Franklin)

M, W: 10:30am - 11:45am | Course website*Forced oscillation and resonance; coupled oscillators and normal modes; Fourier series; Electromagnetic waves, radiation, longitudinal oscillations, sound; traveling waves; signals, wave packets and group velocity; two- and three-dimensional waves; polarization; geometrical and physical optics; interference and diffraction. Optional topics: Water waves, holography, x-ray crystallography, solitons, music, quantum mechanics, and waves in the early universe. *

**PHYSICS 16 - Mechanics and Special Relativity** (Howard Georgi, Amir Yacoby, Carey Witkov, Keith Zengel)

T, TH: 12:00pm - 1:15pm | Course website *Newtonian mechanics and special relativity for students with good preparation in physics and mathematics at the level of the advanced placement curriculum. Topics include oscillators damped and driven and resonance (how to rock your car out of a snow bank or use a swing), an introduction to Lagrangian mechanics and optimization, symmetries and Noether's theorem, special relativity, collisions and scattering, rotational motion, angular momentum, torque, the moment of inertia tensor (dynamic balance), gravitation, planetary motion and a little glimpse of quantum mechanics. *

**PHYSICS 19 - Introduction to Theoretical Physics** (Jacob Barandes)

M, W, F: 3:00pm - 4:15pm | Course website *A comprehensive introduction to the foundations of theoretical physics, with a first-principles approach to its five main areas: analytical dynamics, fields, statistical mechanics, relativity, and quantum theory. Specific topics and examples will include Newtonian mechanics, chaos, celestial mechanics, electromagnetism, the Lagrangian and Hamiltonian formulations, the connection between symmetries and conservation laws, relativistic gravitation, black holes, and quantum information. In-class discussions will regularly address relevant issues in the history and philosophy of physics, as well as the conceptual implications of our modern physical theories for making sense of the world around us. *

**PHYSICS 90R - Supervised Research** (David J. Morin)

Course website *Primarily for selected concentrators in Physics, or in Chemistry and Physics, who have obtained honor grades in Physics 15 and a number of intermediate-level courses. The student must be accepted by some member of the faculty doing research in the student's field of interest. The form of the research depends on the student's interest and experience, the nature of the particular field of physics, and facilities and support available. Students wishing to write a senior thesis can do so by arranging for a sponsor and enrolling in this course. *

**PHYSICS 91R - Supervised Reading Course for Undergraduates** (David J. Morin)

Course website *Open to selected concentrators in Physics, Chemistry and Physics, and other fields who wish to do supervised reading and studying of special topics in physics. Ordinarily such topics do not include those covered in a regular course of the Department. Honor grades in Physics 15 and a number of intermediate-level courses are ordinarily required. The student must be accepted by a member of the faculty*

**PHYSICS 95 - Topics in Current Research** (Eric Mazur)

M: 3:00pm - 4:15pm; W: 7:30pm - 8:45pm | Course website *Open to selected concentrators in Physics, Chemistry and Physics, and other fields who wish to do supervised reading and studying of special topics in physics. Ordinarily such topics do not include those covered in a regular course of the Department. Honor grades in Physics 15 and a number of intermediate-level courses are ordinarily required. The student must be accepted by a member of the faculty. *

**PHYSICS 123 - Laboratory Electronics** (Tom Hayes, David Abrams)

option 1: T, TH: 1:30pm - 5:45pm

option 2: W, F: 1:30pm - 5:45pm

Course website*A lab-intensive introduction to electronic circuit design. Develops circuit intuition and debugging skills through daily hands-on lab exercises, each preceded by class discussion, with minimal use of mathematics and physics. Moves quickly from passive circuits, to discrete transistors, then concentrates on operational amplifiers, used to make a variety of circuits including integrators, oscillators, regulators, and filters. The digital half of the course treats analog-digital interfacing, emphasizes the use of microcontrollers and programmable logic devices (PLDs). *

**PHYSICS 143A - Quantum Mechanics I** (Girma Hailu)

T, TH: 10:30am - 11:45am | Course website*Introduction to nonrelativistic quantum mechanics: uncertainty relations; Schrödinger equation; Dirac notation; matrix mechanics; one-dimensional problems including particle in box, tunneling, and harmonic oscillator; angular momentum, hydrogen atom, spin, Pauli principle; and if time allows: time-independent perturbation theory; and scattering. *

**PHYSICS 143B - Quantum Mechanics II** (Daniel Jafferis)

W, F: 1:30pm - 2:45pm | Course website*Introduction to path integrals, identical particles, many-electron theory, WKB approximation, time-dependent perturbation theory, scattering theory, and relativistic quantum mechanics. *

**PHYSICS 144 - Symmetries and Geometry in Quantum Mechanics** (Eugene Demler)

M, W: 12:00pm - 1:15pm | Course website*This course will review the role of symmetries in quantum mechanics. Topics include atomic and molecular symmetries, crystallographic symmetries, spontaneous symmetry breaking and phase transitions, geometrical Berry phases, topological aspects of condensed matter systems. Mathematical basics of group theory will be taught as needed to give students an understanding of the topics covered. *

**PHYSICS 145 - Elementary Particle Physics **(Roxanne Guenette)

W, F: 10:30am - 11:45am | Course website*Introduction to elementary particle physics. Emphasis on concepts and phenomenology rather than on detailed calculational development of theories. Starts with the discovery of the electron in 1897 and ends with the theoretical motivations for the Higgs boson, and attempts to cover everything important in between. Students will also have a brief experience of particle physics research using Atlas experiment open data. *

**PHYSICS 151 - Mechanics **(Masahiro Morii)

T, TH: 12:00pm - 1:15pm | Course website*Fundamental ideas of classical mechanics including contact with modern work and applications. Topics include Lagrange's equations, the role of variational principles, symmetry and conservation laws, Hamilton's equations, Hamilton-Jacobi theory and phase space dynamics. Applications to celestial mechanics, quantum mechanics, the theory of small oscillations and classical fields, and nonlinear oscillations, including chaotic systems presented. *

**PHYSICS 191 - Advanced Laboratory** (Isaac F. Silvera, Mara Prentiss)

T, TH: 1:30pm - 5:45pm | Course website*Students carry out three experimental projects selected from those available representing condensed matter, atomic, nuclear, and particle physics. Included are pulsed nuclear magnetic resonance (with MRI), microwave spectroscopy, optical pumping, Raman scattering, scattering of laser light, nitrogen vacancies in diamond, neutron activation of radioactive isotopes, Compton scattering, relativistic mass of the electron, recoil free gamma-ray resonance, lifetime of the muon, studies of superfluid helium, positron annihilation, superconductivity, the quantum Hall effect, properties of semiconductors, and plasma physics. The facilities of the laboratory include several computer controlled experiments as well as computers for analysis. *

**PHYSICS 195 - Introduction to Solid State Physics** (Julia Mundy)

M, W: 3:00pm - 4:15pm | Course website*The physics of crystalline solids and their electric, magnetic, optical, and thermal properties. Designed as a first course in solid-state physics. Topics: free electron model; Drude model; the physics of crystal binding; crystal structure and vibration (phonons); electrons in solids (Bloch theorem) and electronic band structures; metals and insulators; semiconductors (and their applications in pn junctions and transistors); plasmonic excitations and screening; optical transitions; solid-state lasers; magnetism, spin waves, magnetic resonance, and spin-based devices; dielectrics and ferroelectrics; superconductivity, Josephson junctions, and superconducting circuits; electronic transport in low-dimensional systems, quantum Hall effect, and resonant tunneling devices. *

**PHYSICS 212 - Cosmology** (Cora Dvorkin)

T, TH: 10:30am - 11:45am | Course website*Standard cosmological model and inflation, scalar inflationary models, cosmological perturbation theory, brief introduction to quantum fields on cosmological backgrounds, interactions and in-in (Keldysh-Schwinger) perturbation theory, non-gaussianities, symmetries and cosmological Ward identities. *

**PHYSICS 223 - Electronics for Scientists**: *see* PHYSICS 123

**PHYSICS 247 - Laboratory Course in Contemporary Physics**: *see* PHYSICS 191

**PHYSICS 251A - Advanced Quantum Mechanics I** (John Doyle)

M, W: 3:00pm - 4:15pm | Course website

Basic course in nonrelativistic quantum mechanics. Review of wave functions and the Schrödinger Equation; Hilbert space; the WKB approximation; central forces and angular momentum; electron spin; measurement theory; the density matrix; perturbation theory.

**PHYSICS 253A - Quantum Field Theory I** (Matthew D. Schwartz)

T, TH: 1:30pm - 2:45pm | Course website*Introduction to relativistic quantum field theory. This course covers quantum electrodynamics. Topics include canonical quantization, Feynman diagrams, spinors, gauge invariance, path integrals, ultraviolet and infrared divergences, renormalization and applications to the quantum theory of the weak and gravitational forces. *

**PHYSICS 253CR - Quantum Field Theory III** (Matthew Reece)

T, TH: 1:30pm - 2:45pm | Course website*Selected advanced topics in quantum field theory, including, but not necessarily limited to: instantons, bosonization, anomalies, confinement, magnetic monopoles, large N expansions, and generalized global symmetries.*

**PHYSICS 262 - Statistical Mechanics** (David R. Nelson)

M, W, F: 12:00pm - 1:15pm | Course website*Basic principles of statistical physics and thermodynamics, with applications including: the equilibrium properties of classical and quantum gases; phase diagrams, phase transitions and critical phenomena, as illustrated by the liquid-gas transition and simple magnetic models. Time permitting, introduction to Langevin dynamics and polymer physics. *

**PHYSICS 268AR - Special Topics in Quantum Matter** (Ashvin Vishwanath)

F: 3:00pm - 5:45pm | Course website*This is a special topics course on quantum systems of many particles, i.e. quantum matter. Primarily, we will be interested in condensed matter systems - eg. electrons in solids or ultra-cold atoms in optical lattices - although the concepts invoked will be more generally applicable. Mostly, we will study well defined microscopic models, involving a finite number of degrees of freedom per unit volume, such as spins on a lattice. Our aim will be to understand the physics at much longer scales, where rich phenomena described by universal laws emerge. Simple spin models will be shown, at long distances, to give rise to remarkable new excitations, from `sound’ and `light’, to fermions and even more exotic excitations. Often, (but not always) we will use quantum field theory to describe this physics, which may also help demystify the origin of quantum field theory in a physical setting free from 'infinities.'*

**PHYSICS 283B - Spacetime and Quantum Mechanics, Total Positivity and Motives** (Nima Arkani-Hamed)

T, TH: 12:00pm - 1:15pm | Course website*Spacetime and Quantum Mechanics form the pillars of our understanding of modern physics, but there are several indications that these concepts must emerge from deeper principles, undoubtedly involving new physics and mathematics. In this course I aim to give a first systematic introduction to some ideas along these lines that have emerged over the past decade. I will present a new formulation of some very basic physics-- fundamental to particle scattering amplitudes and to cosmology--not following from quantum evolution in space-time, but instead associated in a surprising way to new mathematical structures, ranging from the combinatorics and geometry of total positivity and cluster algebras, to period integrals and mixed motives. In these examples, we can concretely see how the usual rules of space-time and quantum mechanics can arise, joined at the hip, from fundamentally geometric and combinatorial origins. The course will be self-contained and should be accessible to physicists and mathematicians alike, with all the relevant physical and mathematical ideas introduced and developed from the ground up. *

**PHYSICS 285B - Modern Atomic and Optical Physics II** (Mikhail Lukin)

M, W: 10:30am - 11:45am | Course website*Introduction to quantum optics and modern atomic physics. The basic concepts and theoretical tools will be introduced. Topics will include coherence phenomena, non-classical states of light and matter, atom cooling and trapping and atom optics. The second of a two-term subject sequence that provides the foundations for contemporary research. *

**PHYSICS 287A - Introduction to String Theory** (Xi Yin)

T, TH: 3:00pm - 4:15pm | Course website*Introduction to the perturbative formulation of string theories and dualities. Quantization of bosonic and superstrings, perturbative aspects of scattering amplitudes, supergravity, D-branes, T-duality and mirror symmetry. Also a brief overview of recent developments in string theory.*

**PHYSICS 289R -Topics in Mathematical Physics** (Tai Wu)

T, TH: 1:30pm - 2:45pm | Course website*Seven years ago, the Higgs particle was discovered by the ATLAS and the CMS Collaborations at CERN. This course gives an introduction to the Englert-Brout-Higgs mechanism and the Higgs particle. *

**PHYSICS 295A - Introduction to Quantum Theory of Solids** (Subir Sachdev)

M, W: 9:00am - 10:15am | Course website*Introduction to the perturbative formulation of string theories and dualities. Quantization of bosonic and superstrings, perturbative aspects of scattering amplitudes, supergravity, D-branes, T-duality and mirror symmetry. Also a brief overview of recent developments in string theory.*

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** Freshman Seminars**

**FRSEMR 21V - Black Holes, String Theory and the Fundamental Laws of Nature** (Andrew Strominger)

W: 6:00pm - 8:30pm | Course website*The quest to understand the fundamental laws of nature has been ongoing for centuries. This seminar will assess the current status of this quest. In the first five weeks we will cover the basic pillars of our understanding: Einstein’s theory of general relativity, quantum mechanics and the Standard Model of particle physics. We will then examine the inadequacies and inconsistencies in our current picture, including for example the problem of quantum gravity, the lack of a unified theory of forces, Dirac’s large numbers problem, the cosmological constant problem, Hawking’s black hole information paradox, and the absence of a theory for the origin of the universe. Attempts to address these issues and move beyond our current understanding involve a network of intertwined investigations in string theory, M theory, inflation and non-abelian gauge theories and have drawn inspiration from the study and observation of black holes, gravitational waves and developments in modern mathematics. These forays beyond the edge of our current knowledge will be reviewed and assessed. *

**FRSEMR 26J - The Universe's Hidden Dimensions** (Lisa Randall)

W: 3:00pm - 5:00pm | Course website*This seminar will give an overview and introduction to modern physics and cosmology. As with the books, Warped Passages, Knocking on Heaven’s Door, Higgs Discovery, and Dark Matter and the Dinosaurs, on which it will be loosely based, the seminar will consider important developments in physics today and in the last century. We will consider the revolutionary developments of quantum mechanics and general relativity; and will investigate the key concepts which separated these developments from the physical theories which previously existed. We will then delve into modern particle physics and cosmology and how theory and experiment culminated in the "Standard Model of particle physics" which physicists use today as well as the current cosmological model based on the Big Bang theory and inflation. We will also move beyond the standard theories into more speculative arenas, including supersymmetry, string theory, and theories of extra dimensions of space, as well as ideas about the nature of dark matter. We will consider the motivations underlying these theories, their current status, and how we might hope to test some of the underlying ideas in the near future. *

**FRSEMR 22S - Quantum Mechanics Face to Face** (Melissa Franklin)

TH: 3:00pm - 5:30pm | Course website*This course is for students who would like to be introduced to the ideas of quantum mechanics without the rigor of mathematics but who would be interested in learning by demonstration as well as spoken word and picture. We will be guided by a non-mathematical text *Introducing Quantum Theory*, read short pieces by the creators of quantum theory, including Bohr, Einstein, Heisenberg and Schrodinger, and each week watch and play with physics demonstrations of wave and particle physics. This course requires reading, watching short films, watching demonstrations in the lab and visiting places at the university where quantum mechanics is used on a daily basis.*

**FRSEMR 23Y - All Physics in 13 Days** (John Doyle)

TH: 6:00pm - 8:45pm | Course website*Some claim that there are 13 ideas or principles that can form the bedrock for a pretty good understanding of our physical and technological world. These are: 1) Boltzmann factor and thermal equilibrium, 2) Turbulence, 3) Reaction rates, 4) Indistinguishable particles, 5) Quantum waves, 6) Linearity, 7) Entropy and information, 8) Discharges, ionization, 9) Relativity, 10) Nuclear binding energies, 11) Photon modes, 12) Diffraction, 13) Resonance. Each week we will discuss one of these principles and see how they explain certain things about the physical world. We will discuss these and connections with other principles, as well as how the principle shows up in technology and, more broadly, in our technological society. *

**FRSEMR 23P - Physics, Math and Puzzles** (Cumrun Vafa)

TH: 6:00pm - 8:00pm | Course website*Physics is a highly developed branch of science with a broad range of applications. Despite the complexity of the universe the fundamental laws of physics are rather simple, if viewed properly. This seminar will focus on intuitive as well as mathematical underpinnings of some of the fundamental laws of nature. The seminars will use mathematical puzzles to introduce the basic features of physical laws. Main aspects discussed include the role of symmetries as well as the power of modern math, including abstract ideas in topology, in unraveling the mysteries of the universe. Examples are drawn from diverse areas of physics including string theory. The issue of why the universe is so big, as well as its potential explanation is also discussed.*