# Graduate Studies - Courses

## Courses - *Please note: some courses are not offered every year, please see Yale Course Search for current course offerings*

### Physics 500, Advanced Classical Mechanics

Newtonian dynamics and kinematics, Lagrangian dynamics, small oscillations, Hamiltonian dynamics and transformation theory, completely integrable systems, regular and chaotic motion of Hamiltonian systems, mechanics of continuous systems: strings and fluids.

### Physics 502, Electromagnetic Theory I

Classical electromagnetic theory including boundary value problems and applications of Maxwell equations. Macroscopic description of electric and magnetic materials. Wave propagation.

### Physics 504L, Modern Physics Measurements

A laboratory course with experiments in atomic, condensed matter, nuclear, and elementary particle physics. Data analysis provides an introduction to computer programming and to the elements of statistics and probability.

### Physics 506, Mathematical Methods of Physics

Survey of mathematical techniques useful in physics. Includes vector and tensor analysis, group theory, complex analysis (residue calculus, method of steepest descent), differential and integral equations (regular singular points, Green’s functions), and advanced topics (Grassmann variables, path integrals, supersymmetry.

### Physics 508, Quantum Mechanics I.

The principles of quantum mechanics with application to simple systems. Canonical formalism, solutions of Schrodinger’s equation, angular momentum and spin.

### Physics 510, Quantum Mechanics II

Approximation methods, scattering theory and the role of symmetries. Relativistic wave equations. Second quantized treatment of identical particles. Elementary introduction to quantized fields.

### Physics 512, Statistical Physics I

Review of thermodynamics, the fundamental principles of classical and quantum statistical mechanics, canonical and grand canonical ensembles, identical particles, Bose and Fermi statistics, phase-transitions and critical phenomena, renormalization group, irreversible processes, fluctuations.

### Physics 515, Topics in Modern Physics Research

A seminar course intended to provide an introduction to current research in physics and an overview of physics research opportunities at Yale.

### Physics 522, Introduction to Atomic Physics

This course is intended to develop basic theoretical tools needed to understand fundamental atomic processes. Emphasis given to applications in laser spectroscopy. Experimental techniques discussed when appropriate.

### Physics 523, Biological Physics

An introduction to the physics of biological systems, including molecular motors, protein folding, membrane self-assembly, ion pumping, and bacterial locomotion. Background concepts in probability and statistical mechanics are introduced as necessary, as well as key constituents of living cells.

### Physics 524, Introduction to Nuclear Physics

Introduction to a wide variety of topics in nuclear structure, nuclear reactions, and nuclear physics at extremes of angular momentum, isospin, energy, and energy density.

### Physics 525, Quantum Physics at Femto- and Nano-scales

Classical and quantum field theories, symmetries and their breakdown, dynamics of collective excitations, renormalization group, weak coupling methods, quasi-classical approximation, topological effects, phase transitions and critical phenomena. A wide range of examples and applications will be presented, including Quantum Chromo-Dynamics, quark-gluon plasma, nuclear structure, nano-scale systems (especially graphene and carbon nano-tubes), physics of black holes and the Early Universe.

### Physics 526, Introduction to Elementary Particle Physics

An overview of particle physics including a historical introduction to the standard model, experimental techniques, symmetries, conservation laws, the quark-parton model, and a semiformal treatment of the standard model.

### Physics 538, Introduction to Relativistic Astrophysics and General Relativity.

Basic concepts of differential geometry (manifolds, metrics, connections, geodesics, curvature); Einstein’s equations and their application to cosmology, gravitational waves, black holes, etc.

### Physics 548 and 549, Solid State Physics I and II

A two-term sequence covering the principles underlying the electrical, thermal, magnetic, and optical properties of solids, including crystal structures, phonon, energy bands, semiconductors, Fermi surfaces, magnetic resonance, phase transitions, and superconductivity. Also E&AS 850au,851bu.

### Physics 602, Classical Field Theory

Covariant formulation of electrodynamics as an example of a classical relativistic field theory. Lagrangian formalism, symmetries and conservation laws, nonlinear phenomena. Introduction to general relativity and other classical field theories.

### Physics 609, Relativistic Field Theory I

The fundamental principles of quantum field theory. Interacting theories and the Feynman graph expansion. Quantum electrodynamics including lowest order processes, one loop corrections, and the elements of renormalization theory.

### Physics 610, Quantum Many-Body Theory I

Second quantization, quantum statistical mechanics, Hartree-Fock approximation, linear response theory, random phase approximation, perturbation theory and Feynman diagrams, Landau theory of Fermi liquids, BCS theory, Hartree-Fock-Bogoliubov method. Applications to solids and finite-size systems such as quantum dots, nuclei, and nanoparticles.

### Physics 624, Group Theory

Lie algebras, Lie groups and some of their applications. Representation theory. Explicit construction of finite-dimensional irreducible representations. Invariant operators and their eigenvalues. Tensor operators and enveloping algebras. Boson and fermion realizations. Differential realizations. Quantum dynamical applications.

### Physics 628, Statistical Physics II

An introduction to topics in many-body physics, namely, Ising models, transfer matrix, critical phenomena, renormalization group in critical phenomena and field theory, sigma models, and bosonization.

### Physics 630, Relativistic Field Theory II

An introduction to nonabelian gauge field theories, spontaneous symmetry breakdown and unified theories of weak and electromagnetic interactions. Renormalization group methods, quantum chromodynamics, and nonperturbative approaches to quantum field theory.

### Physics 631, Computational Physics I

A laboratory course on modern numeric computational techniques with applications to science problems of current interest. Topics include data analysis, numerical integration, solutions to differential equations, and Monte Carlo techniques. Previous experience with a computer programming language is desirable. Some applications will use Mathematica.

### Physics 632, Quantum Many-Body Theory II

A second course in quantum many-body theory, covering the core physics of electron systems, with emphasis on the electron-electron interaction, on the role of dimensionality, on the coupling either to magnetic impurities leading to the well-known Kondo effect or to the electromagnetic noise. Applications to mesoscopic systems and cold atomic gases are also developed.

### Physics 633, Introduction to Superconductivity

The fundamentals of superconductivity, including both theoretical understandings of basic mechanism and description of major applications. Topics include historical overview, Ginzburg-Landau (mean field) theory, critical currents and fields of type ii superconductors, BCS theory, Josephson junctions and microlectronic and quantum-bit devices, and high Tc oxide superconductors.

### Physics 634, Mesoscopic Physics I

Introduction to the physics of nanoscale solid state systems that are large and disordered enough to be described in terms of simple macroscopic parameters like resistance, capacitance, and inductance, but small and cold enough that effects usually associated with microscopic particles, like quantum-mechanical coherence and/or charge quantization, dominate. Emphasis is placed on transport and noise phenomena in the normal and superconducting regimes.

### Physics 650 and 651, Theory of Solids I and II

Theoretical techniques for the studyof the structural and electronic properties of solids, with applications. Topics include band structure, phonons, defects, transport, magnetism, and superconductivity.

## Special Topics Courses

### Physics 661, The Art of Data Analysis

The course is an introduction to mathematical and statistical techniques used to analyse data. The course is fairly practice-oriented, and is aimed at students who have, or anticipate having, research data to analyze in a thorough and unbiased way. It will cover subjects in statistics, computing/numerical techniques, data analysis, but also topics related to data reconstruction and pattern recognition which are closely linked to the understanding of the data derived from those methods. The intention is to prepare students for a better approach to their own analysis. Many of the topics covered are related to typical problems in experimental high energy and nuclear physics but are fairly general in nature. If you are interested please contact: thomas.ullrich@bnl.gov.

### Physics 662, Special Topics in Particle Physics: Beyond the Standard Model

By arrangement with faculty.

Modern concepts in particle physics, including electroweak symmetry breaking, mass generation, conformal symmetry, strongly coupled quantum field theories, supersymmetry, and extra dimensions. Material covered includes the theoretical basis of these ideas, experimental tests and constraints, and implications for cosmology.

### Physics 663, Special Topics in Cosmology and Particle Physics

By arrangement with faculty.

### Physics 664, Special Topics in Nuclear Electromagnetic Interactions

By arrangement with faculty.

### Physics 664, Special Topics in Nuclear Physics

Emphasis is on nuclear structure. The approach stresses physical ideas, leading to an understanding of a number of advanced nuclear models and to practical case studies with them.

### Physics 665, Special Topics in Atomic Physics

By arrangement with faculty.

### Physics 666, Special Topics in Classical Field Theory

By arrangement with faculty.

### Physics 667/G&G 767, Special Topics in Condensed Matter Physics

*Seminar in Ice Physics and Geophysics/John Wettlaufer*

This seminar brings together the basic thermodynamics and statistical mechanics of crystal growth, surface phase transitions, metastability and instability to explore the many faces of the surface of ice. The motivating factor is the incommensurability between the length of the history of observations of the shapes of snow crystals (which begins in ancient China, continues with Kepler’s little known studies of 1611, and carries on from Descartes to the present day) and our continued ignorance concerning the physical processes that are responsible for those shapes. Those processes are unique insofar as we understand that microphysics is clearly controlling macroscopic shapes. The outstanding question is how? The prize of understanding these processes extends beyond the enigma of the snowflake, having implications in, inter alia, the atmosphere ranging from radiative transfer to the heterogenous chemistry in the polar stratosphere, to materials processing and applied mathematics. The seminar will be driven by the literature, which spans periodicals in many branches of physical science and engineering, and will be a journal club environment.

### Physics 667, Special Topics in Condensed Matter Physics

An introduction to nonequilibrium statistical mechanics in classical and quantum systems. Brief survey of equilibrium physics and processes, Green-Kubo theory, and approaches ranging from those of Kawasaki to Zubarev. The relation of dynamical systems and chaos to statistical mechanics and transport. Discussion of open problems and applications.

### Physics 668, Special Topics in Geometry and Modern Field Theory

By arrangement with faculty

Explores the relation between modern geometry and (supersymmetric) gauge theories. Topics include a survey of fiber bundles, connections, holonomy, characteristic classes, Dirac operators, and the supersymmetric proofs of the index theorems.

### Physics 671, Special Topics in Experimental Nuclear and Particle Physics

Propagation of particles and photons in matter, modern detection techniques, types of detectors, large detector systems, accelerators, and seminal experiments are studied. The subject spans the range of energies from low energy nuclear physics up through high energy physics.

### Physics 672, Special Topics in Experimental Physics

By arrangement with faculty.

### Physics 673, Special Topics in Atomic Physics

By arrangement with faculty.

### Physics 674, Quantum Information, Quantum Cryptography, and Quantum Computation

The basic principles of quantum information, cryptography, and computation will be covered. Following the theoretical introduction, methods of realizing real world devices will be discussed. These will encompass methods based on both atomic/molecular systems and solid state systems. Lecture section of the course as described will take approximately half the class time; the remaining time will be devoted to student presentations of selected papers.

### Physics 675, Principles of Optics with Applications

Introduction to the principles of optics and electromagnetic wave phenomena with applications to microscopy, optical fibers, laser spectroscopy, nanophotonics, plasmonics and metamaterials. Topics included propagation of light, reflection and refraction, guiding light, polarization, interference, diffraction, scattering, Fourier optics, and optical coherence.

### Physics 680, The Experiments of General Relativity

The basic physical ideas and mathematical formulation of general relativity are reviewed, although many results that apply to particular experiments are given without proof. The modern experiments that make precision tests of the theory are explained. These include lunar laser ranging, radar timing from planet Venus reflections, and gravitational radiation from a binary pulsar. A discussion of the LIGO experiment (earth-based gravity wave detector) and LISA (space-based gravity wave detector) is conducted. The course is open to upper-level undergraduates as well as graduate students.