Local Reference Frame

Students are encouraged to participate in the comprehensive set of courses offered. A limited number of core courses are required as part of the general examination.

PHY 501 Electricity and Magnetism

William Happer

A systematic treatment of the theory of electromagnetic phenomena from an advanced standpoint. Maxwell’s equations are discussed, with special attention given to their physical meaning. Other topics include dielectric and magnetic media, radiation, scattering, potential theory, and waves in simple media.

PHY 505 Quantum Mechanics I

Robert Seiringer

The physical principles and mathematical formalism of non-relativistic quantum mechanics. The principles are illustrated by selected applications to topics in atomic physics, particle physics, and condensed matter.

PHY 506 Quantum Mechanics II

Elliott Lieb

A one-term course in advanced quantum mechanics, following PHY 505. After a brief review of some fundamental topics (e.g., the hydrogen atom, perturbation theory), more advanced topics are covered, including many-body theory, operator theory, coherent states, stability of matter and other Coulomb systems, and the theory of the Bose gas.

PHY 509 Relativistic Quantum Theory I

Alexander Polyakov

Introduction to quantum field theory. Quantization of Klein-Gordon and Dirac fields. Interactions with Feynman diagrams. Elementary processes in quantum electrodynamics. Introduction to non-abelian gauge theory. Radiative corrections.

PHY 510 Relativistic Quantum Theory II

Steve Gubser

Advanced topics in Relativistic Quantum Theory: renormalization group, non-perturbative techniques (solitons, instantons), and quantum fields in curved space.

PHY 511 Thermodynamics, Kinetic Theory, and Statistical Mechanics

F. Duncan Haldane

The physical principles and mathematical formalism of statistical mechanics, with an emphasis on applications to thermodynamics, condensed-matter physics, physical chemistry, and astrophysics are studied.

PHY 521 Introduction to Mathematical Physics

Robert Seiringer

An introduction to mathematically rigorous methods in physics, mainly in the area of quantum statistical mechanics. Possible topics include the study of thermodynamic limits, phase transitions, spontaneous symmetry breaking, Bose-Einstein condensation and superfluidity. Both lattice and continuous systems will be considered.

PHY 523 Introduction to Relativity

Igor Klebanov

A modern introduction from scratch to the theory of gravity, with an emphasis on quantum effects, supersymmetry, strings, and black holes.

PHY 525, 526 Introduction to Condensed-Matter Physics (also MSE 516, 517)

David Huse, Shivaji Sondhi

In the fall term, the course explores electronic structure of crystals, phonons, transport and magnetic properties, screening in metals, and superconductivity. In the spring, the focus is on “soft” condensed-matter physics, including fluids, polymers, interfaces, membranes, liquid crystals, the dynamics of phase transitions, generalized elasticity, dislocations, and hydrodynamics.

PHY 529 Introduction to High-Energy Physics

Norman C. Jarosik , Christopher Tully

An overview of modern elementary particle physics. The basic formalism is developed in the context of quantum electrodynamics (QED), then the principle of local gauge invariance is used to generalize to the current Standard Model of the fundamental interactions. The latter is then applied to a variety of phenomena, including weak decays, W and Z physics, deep inelastic scattering, CP violation, neutrino oscillations, and Higgs searches, with an emphasis on areas of current interest. The course also covers key concepts in accelerator and detector physics.

PHY 535 Condensed-Matter/Many-Body Physics

Staff

The course is planned as an introduction to the modern quantum theory of condensed matter. We discuss properties of both Bose and Fermi quantum liquids, and phenomena such as Bose-Einstein condensation, superfluidity and superconductivity of various systems. We also consider effects of the Coulomb interaction between the quantum particles and quenched disorder. We discuss both equilibrium and transport properties of bulk as well as low-dimensional quantum liquids. Special attention is paid to the zero-dimensional case—i.e., finite size (mesoscopic) systems. The course is focused on the qualitative physics and basic concepts rather than on technical details. A more technically advanced description is planned for the spring term course.

PHY 539 Selected Topics in High-energy Physics: Introduction to String Theory

Lian-Tao Wang

The large N expansion in gauge theories; quantization of closed and open strings; string perturbation theory and conformal field theory techniques; string effective actions; and large N matrix models and random surfaces.

PHY 540 Selected Topics in Theoretical High-Energy Physics: Strings, Membranes, and Gauge Theories

Staff

Superstrings; low-energy effective actions; p-brane solutions in supergravity; Dirichlet branes; D-brane approach to black holes; the AdS/CFT correspondence.

PHY 542 Beyond the Standard Model

Steven S. Gubser, Christopher G. Tully

Course aims to survey some of the proposed answers to the following questions, and their consequences: What lies beyond the Standard Model of particle physics? What new particles or interactions will we find at TeV energies and above? Why does the Standard Model have the characteristic energy scales that it has, and the spectrum of particles that we observe?

PHY 557 Electronic Methods in Experimental Physics

Norman C. Jarosik, Christopher Tully

Students learn how to instrument and read out an experimental apparatus with analog and digital circuits. No advanced knowledge of electronics is required in order to begin. The first half covers analog components such as RC circuits, amplifiers, photodiodes, accelerometers, and audio. The second focuses on digital logic, gates and flip-flops, buses, microcontrollers, and programmable FPGAs. Students build in the laboratory roughly 40 different and unique circuits.

PHY 561, 562 Biophysics

Robert H. Austin, William Bialek

A physicist’s perspective on selected topics in biology. Explores problems ranging from functioning of individual biological molecules and their complexes to emerging collective properties of biological systems.

PHY 563, 564 Physics of the Universe: Origin and Evolution

Paul J. Steinhardt

A two-semester survey of the fundamental concepts that underlie contemporary cosmology. The first semester focuses on the nearly homogeneous evolution of the universe, including the standard big bang picture, inflationary cosmology, dark matter, and the possibility of present-day accelerated expansion. The second focuses on the late stages in the evolution of the universe, when gravity results in the growth of large-scale structure, perturbations in the cosmic microwave background, gravitational lensing, and other nonlinear phenomena.

PHY 567 Advanced Solid-State Electron Physics (see ELE 567)

PHY 570 Method and Logic in Quantitative Biology (see MOL 515)

PHY 580 Extramural Summer Research Project

Chiara Nappi

Summer research project designed in conjunction with the student’s adviser and an industrial, NGO, or government sponsor who will provide practical experience relevant to the student’s research area. Start date no earlier than June 1. A research report and a sponsor’s evaluation are required.

PHY 581 Extramural Research Internship

Chiara Nappi

Full-time research internship at a host institution to perform scholarly research directly relevant to a student’s dissertation work. Research objectives are determined by the student’s adviser in consultation with the outside host. Monthly progress reports and a final paper are required. Enrollment is limited to post-generals students, for a period of no more than one academic year (two terms). Participation will be considered exceptional.


2. Harvard University

http://www.registrar.fas.harvard.edu/Courses/Physics.html

Primarily for Graduates

The courses primarily for graduates are open to undergraduates provided they have passed the prerequisites with a grade of C or higher; in each case, special permission by the instructor is needed. In cases where students do not have the listed prerequisites, the written approval of the Head Tutor is required.

Physics 210. General Theory of Relativity
Catalog Number: 4840
Andrew Strominger
Half course (fall term). W., F., 2:30–4. EXAM GROUP: 7, 8
An introduction to general relativity: Riemannian geometry; the Principle of Equivalence; Einstein’s field equation; the Schwarzchild solution, the Newtonian limit; experimental tests, black holes, the causal structure of spacetime.
Prerequisite: Physics 151 and 153, and Mathematics 21 or equivalents.

Physics 211. General Relativity, Cosmology, and Other Topics
Catalog Number: 0469
Frederik Denef
Half course (spring term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14
The course consists of two related parts: quantum field theory in curved space and cosmology. Topics covered in the first part include mode expansions, Bogolubov transformations, the Unruh effect, Hawking radiation, black hole thermodynamics, de Sitter thermodynamics, fluctuation spectra in inflationary universes, vacuum energy and the Casimir effect. Topics in the second part include kinematics and dynamics of expanding universe, propagation of light and horizons, the (very) early universe, inflation, inhomogeneities and structure formation.
Prerequisite: General relativity at level of Physics 210 or equivalent. Physics 253a helpful, but not required.

[Physics 218. Modern Dynamical Systems]
Catalog Number: 1362
Instructor to be determined
Half course (spring term). Hours to be arranged.
Classical hamiltonian theory. Integrable systems, nonlinear dynamics, and chaos. Maps, KAM theory, and bifurcations. Mixing and ergodic theory. Dynamics of continuous systems, especially fluids. Stochastic processes.
Note: Expected to be given in 2010–11.
Prerequisite: Physics 151 and 143a, b or equivalent; Applied Math 201, 202 or equivalent.

Physics 232 (formerly Physics 232a). Advanced Classical Electromagnetism
Catalog Number: 4885
David R. Nelson
Half course (spring term). M., W., F., at 10. EXAM GROUP: 3
Maxwell’s equations in free space and in macroscopic media; conservation laws; time-dependent solutions and radiation; scattering and diffraction. Additional topics could include dielectric properties of composite media, magnetohydrodynamics or negative refractive index materials.
Prerequisite: Physics 153 and Applied Math 105a, 105b, or equivalent.

*Physics 247r. Laboratory Course in Contemporary Physics
Catalog Number: 8665 Enrollment: Together with Physics 191r, limited to a total of 24 students.
Eric Mazur (spring term), Peter S. Pershan (fall term), Mikhail D. Lukin (spring term), Isaac F. Silvera (fall and spring terms), and Robert M. Westervelt (fall term)
Half course (fall term; repeated spring term). Tu., Th., 1–5. EXAM GROUP: Fall: 15, 16, 17; Spring: 15, 16, 17, 18
Three experimental projects are selected representing condensed matter, atomic, nuclear, and particle physics. Examples: experiments on NMR, microwave spectroscopy, optical pumping, scattering of laser light, neutron activation, Compton scattering of gamma rays, relativistic mass of the electron, recoil-free gamma ray resonance, lifetime of the muon, superfluid helium, superconducting transitions, and properties of semiconductors.
Note: A substantial amount of outside reading may be required.

[Physics 248. Phenomena of Elementary Particle Physics ]
Catalog Number: 5431
Instructor to be determined
Half course (fall term). Hours to be arranged.
Topics in the phenomena of elementary particle physics, including weak interactions, QCD, deep inelastic scattering and nucleon structure functions, and heavy quark production and decay.
Note: Expected to be given in 2010–11.
Prerequisite: Physics 145 or equivalent, i.e. a course at the level of Griffiths, Introduction to Elementary Particles.

Physics 251a. Advanced Quantum Mechanics I
Catalog Number: 2191
Bertrand I. Halperin
Half course (fall term). M., W., F., at 12. EXAM GROUP: 5
Basic course in nonrelativistic quantum mechanics. Review of wave functions and the Schrödinger Equation; Hilbert space; the WKB approximation; central forces and angular momentum; scattering; electron spin; measurement theory; the density matrix; time-independent perturbation theory.
Prerequisite: Physics 143a, b or equivalent, or permission of instructor.

Physics 251b. Advanced Quantum Mechanics II
Catalog Number: 2689
Bertrand I. Halperin
Half course (spring term). M., W., F., at 12. EXAM GROUP: 5
Heisenberg picture; time-dependent perturbations; inelastic scattering; degenerate harmonic oscillators; electrons in a uniform magnetic field; quantized radiation field; absorption and emission of radiation; identical particles and second quantization; symmetry principles; Feynman Path integrals.
Prerequisite: Physics 251a.

Physics 253a. Quantum Field Theory I
Catalog Number: 8050
Matthew D. Schwartz
Half course (fall term). Tu., Th., 1–2:30. EXAM GROUP: 15, 16
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.
Prerequisite: Physics 143a,b or equivalents.

Physics 253b. Quantum Field Theory II
Catalog Number: 5250
Howard Georgi
Half course (spring term). Tu., Th., 1–2:30. EXAM GROUP: 15, 16
A continuation of Physics 253a. spontaneous symmetry breaking and Goldstone bosons, chiral anomalies, effective field theory, non-Abelian gauge theories, the Higgs mechanism, and an introduction to the standard model, quantum chromodynamics and grand unification. Other possible subjects include solitons, quantum gravity, conformal field theory, supersymmetry and applications to condensed matter physics.
Prerequisite: Physics 253a.

Physics 253c. Quantum Field Theory III
Catalog Number: 4000
Lisa Randall
Half course (fall term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14
This course explores advanced topics in quantum field theory. Possible topics include semi-classical methods, tunneling in flat and curved spaces, topological defects, lattice gauge theories, conformal field theories in diverse dimensions, large N and string description of gauge theory, the AdS/CFT correspondence, and supersymmetric gauge theories in four dimensions.
Prerequisite: Physics 253b.

[Physics 262. Statistical Physics]
Catalog Number: 1157
Instructor to be determined
Half course (fall term). Hours to be arranged.
Basic principles of statistical physics and thermodynamics, with applications including: the equilibrium properties of classical and quantum gases; phase diagrams, phase transitions and critical points, as illustrated by the gas-liquid transition and simple magnetic models; Bose-Einstein condensation. Dynamics near equilibrium: Brownian motion, Langevin, Fokker-Planck and Boltzmann equations.
Note: Expected to be given in 2010–11. Students may wish to take Applied Physics 284 when this course is bracketed.
Prerequisite: Physics 143a, b and Physics 181 or Engineering Sciences 181.

[Physics 268r. Classical and Quantum Phase Transitions]
Catalog Number: 7951
Instructor to be determined
Half course (spring term). Hours to be arranged.
The theory of phase transitions at zero and non-zero temperatures. Landau theory. Fluctuations and field theory. Renormalization group. Quantum transitions between insulators, superfluids, metals, and magnets. Modern ideas on the description of correlated states by emergent gauge fields.
Note: Expected to be given in 2010–11.
Prerequisite: Physics 262 or equivalent.

Physics 269r. Topics in Statistical Physics and Physical Biology
Catalog Number: 6214
Erel Levine
Half course (spring term). M., W., F., at 11. EXAM GROUP: 4
Introduction to strongly interacting soft condensed matter and biophysical systems. We hope to discuss the theory of flexible polymer chains, function and structure of DNA, RNA and proteins, single molecule biophysics, molecular motors, gene regulation and the statistical dynamics of mutations, selection and genetic drift.
Prerequisite: Physics 262, Applied Physics 284 or equivalent.

[Physics 271 (formerly Physics 287). Topics in the Physics of Quantum Information]
Catalog Number: 7647
Instructor to be determined
Half course (fall term). Hours to be arranged.
Introduction to physics of quantum information, with emphasis on ideas and experiments ranging from quantum optics to condensed matter physics. Background and theoretical tools will be introduced. The format is a combination of lectures and class presentations.
Note: Expected to be given in 2010–11.
Prerequisite: Quantum mechanics at the level of introductory graduate courses.

[Physics 283b. Beyond the Standard Model]
Catalog Number: 7153
Instructor to be determined
Half course (fall term). Hours to be arranged.
Covers current advances in particle physics beyond the Standard Model. Topics could include supersymmetry, the physics of extra dimensions, experimental searches, including for T violation, and connections between particle physics and cosmology.
Note: Expected to be given in 2010–11.

Physics 284. Strongly Correlated Systems in Atomic and Condensed Matter Physics
Catalog Number: 4673
Eugene A. Demler
Half course (fall term). Tu., Th., 10–11:30. EXAM GROUP: 12, 13
Explores an emerging interface involving strongly correlated systems in atomic and condensed matter physics. Topics include bosonic and fermionic Hubbard models, quantum spin systems, low dimensional systems, non-equilibrium coherent dynamics and system-bath interactions. Special attention to the physics of ultracold atoms. Lectures and seminar-like class presentations.
Prerequisite: Graduate quantum mechanics or permission of instructor.

[Physics 285a. Modern Atomic and Optical Physics I]
Catalog Number: 8204
Instructor to be determined
Half course (fall term). M.,W., 12-1:30.
Introduction to modern atomic physics. The fundamental concepts and modern experimental techniques will be introduced. Topics will include two-state systems, magnetic resonance, interaction of radiation with atoms, transition probabilities, spontaneous and stimulated emission, dressed atoms, trapping, laser cooling of “two-level” atoms, structure of simple atoms, fundamental symmetries, two-photon excitation, light scattering and selected experiments. The first of a two-term subject sequence that provides the foundations for contemporary research.
Note: Expected to be given in 2010–11.
Prerequisite: One course in quantum mechanics (143a and b, or equivalent).

Physics 285b. Modern Atomic and Optical Physics II
Catalog Number: 4195
Mikhail D. Lukin
Half course (fall term). M., W., 12–1:30. EXAM GROUP: 5, 6
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.
Prerequisite: A course in electromagnetic theory (Physics 232a or equivalent); one half-course in intermediate or advanced quantum mechanics.

Physics 287a. Introduction to String Theory
Catalog Number: 2012
Cumrun Vafa
Half course (spring term). W., F., 2:30–4. EXAM GROUP: 7, 8
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.
Prerequisite: Physics 253a, b or equivalent.

[Physics 287br. Topics in String Theory]
Catalog Number: 4555
Instructor to be determined
Half course (spring term). Hours to be arranged.
A selection of topics from current areas of research on string theory.
Note: Expected to be given in 2010–11.
Prerequisite: Physics 287a.

Physics 289r. Functional Integration and Renormalization
Catalog Number: 6400
Arthur M. Jaffe
Half course (spring term). Tu., Th., 10–11:30. EXAM GROUP: 12, 13
The course will revolve around Euclidean expectations, functional integrals, and real-time quantum theory for bosons, fermions, and gauge interactions, with properties of symmetry, supersymmetry, and renormalization.
Prerequisite: Physics 253a

3. Stanford University

4. California Institue of Technology

http://www.pma.caltech.edu/physicscourses.html

5. MIT

http://web.mit.edu/physics/subjects/index.html

SM by X.G.Wen: http://dao.mit.edu/8.08/