Graduate Studies - Courses

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

Physics 5000, 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 5020, 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 5060, 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 5080, 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 5100, 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 5120, 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 5150, 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 5220, 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 5230, 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 5240, 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 5260, 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 5300, Theory and Practice of Scientific Teaching

The course discusses the fundamentals of learning theory and practical strategies for teaching in the physical and life sciences. Students learn evidence-based teaching strategies, including engaging students through active learning, incorporating inclusive teaching practices, and developing effective assessments, while building a community of scientific educators.

Physics 5380, 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 5450L, 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 5480 and 5490, 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 6030, Euclidean-Signature Semi-Classical Analysis for Quantum Mechanics and Field Theory

The course will cover advanced semi-classical techniques , their applications, and their advantages over traditional quantum mechanical problem-solving methods.

Physics 6100, 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 6120, 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 6150, 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 6200, 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 6240, 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 6300, 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 6330, 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 6340, 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.

PHYS 6350 : Quantum Entanglement in HEP

Basic principles and applications of quantum entanglement and quantum information science at GeV to TeV energies in particle and nuclear physics are covered. Topics include: quantum superposition, quantum entanglement, entanglement entropy, quantum computing, quantum algorithms, Bell’s inequality tests, and quantum sensors.

Physics 6400, Relativistic Field Theory III

Physics 6500, Theory of Solids I

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

Physics 6600, Special Topics in Astrophysics

A multidisciplinary graduate-level course to introduce students to the approaches, methods, major results, and open questions at the intersection between cosmology, particle physics, and astrophysics. The exact focus of this class for any semester varies, but topics include the role of neutrinos, dark matter, the cosmic microwave background, gravity, dark energy, astrophysical observation, cosmology, and particle physics, as well as the experimental, computational, and analytical techniques and methods used to investigate these topics.

Physics 6630, Special Topics in Cosmology and Particle Physics

This course covers various advanced topics in particle theory. Possible topics include symmetries and anomalies, conformal field theories, supersymmetry, and aspects of string theory and the AdS/CFT correspondence. This course assumes knowledge from PHYS 609 but may be taken concurrently with PHYS 6300.

Physics 6650, Graduate Research Seminar

Seminar research presentations by graduate students.

Physics 6670 Special Topics in Condensed Matter Physics

The course is a survey of topics in statistical mechanics, information theory, and the connections between the two, in both classical and quantum cases, treated in an unabashedly mathematical manner. The theme is that unresolved issues—occurring, e.g., in our understanding of spin glasses—involve the use of concepts (such as classical “pure states”) that are well defined only in an infinite lattice system, and which consequently can be handled only with mathematical techniques more advanced than those familiar to most condensed matter or quantum physicists.

Physics 6700, Special Topics in Biophysics

The aim of the course is to introduce students to the approaches, methods, major results, and open questions in modern biological physics. Topics include non-equilibrium statistical physics, with applications to kinetic proof-reading and understanding molecular motors, information theory with applications to cellular signaling and phase transitions as they occur in living systems. The course is designed for graduate students in physics or a closely related field, otherwise, permission of the instructor is required.

Physics 6780, Computing for Scientific Research

This hands-on lab course introduces students to essential computational and data analysis methods, tools, and techniques and their applications to solve problems in physics. The course introduces some of the most important and useful skills, concepts, methods, tools, and relevant knowledge to get started in scientific research broadly defined, including theoretical, computational, and experimental research. Students learn basic programming in Python, data analysis, statistical tools, modeling, simulations, machine learning, high-performance computing, and their applications to problems in physics and beyond.