Course subject: Physics (PHYS)

A brief review of ensembles and quantum gases, Ising model, Landau theory of phase transitions, order parameters, topology, classical solutions.

Special relativity, foundations of general relativity, Riemannian geometry, Einstein's equations, FRW and Schwarzschild geometries and their properties

Probability, entropy, Bayesian inference and information theory. Maximum likelihood methods, common probability distributions, applications to real data including Monte-Carlo methods.

Common algorithms for ode and pde solving, with numerical analysis. Common tasks in linear algebra. Focus on how to write a good code, test it, and obtain a reliable result. Parallel programming.

This course will include the study of Perturbation Theory (Regular and Singular) Speeding Up Convergence: Shanks Transformations and Richardson Extrapolation Taylor Series, Fourier Series and the Gibbs Phenomenon Using Diveregent Series: Generalised Summation Analytic Continuation, Riemann Surfaces and Branch Points Continued Functions and Pade Approximants Steiltjes Functions, the Herglotz Property and the Carleman Bound Feynman Diagrams.

FRW metric, Hubble expansion, dark energy, dark matter, CMB. Thermodynamic history of early universe. Growth of perturbations, CDM model of structure formation and comparison to observations, cosmic microwave background anisotropies, inflation and observational tests.

Superstring spectrum in 10d Minkowski, as well as simple toroidal and orbifold compactifications. T-duality, D-branes, tree amplitudes. Construct some simple unified models of particle physics. Motivate the 10- and 11-dimensional supergravities. Simple supergravity solutions and use these to explore some aspects of AdS/CFT duality.

The following topics will be discussed: The Lorentz Group: Properties and Representations; Manipulating Spinors; Supersymmetry Algebra and Representations; Superfields and Superspace; 4d Supersymmetric Lagrangians; Supersymmetry Breaking; Constructing the MSSM; Collider Phenomenology of Supersymmetric Theories; and Dark Matter.

Review of selected topics in Gravitational Physics

Review of selected topics in Quantum Gravity

Review of selected topics in Quantum Information

Review of selected topics in Condensed Matter Theory

Review of Selected topics in Foundations of Quantum Theory

Review of selected topics in String Theory

Review of Selected topics in Cosmology

Review of formalism of nonrelativistic quantum mechanics including symmetries and invariance. Approximation methods and scattering theory. Elementary quantum theory of radiation. Introduction to one-particle relativistic wave equations.

Review of relativistic quantum mechanics and classical field theory. Quantization of free quantum fields (the particle interpretation of field quanta). Canonical quantization of interacting fields (Feynman rules). Application of the formalism of interacting quantum fields to lowest¿order quantum electrodynamic processes. Radiative corrections and renormalization.

Phase transitions. Fluctuation phenomena. Kubo's theory of time correlation functions for transport and spectral properties; applications selected from a variety of topics including linearized hydrodynamics of normal and superfluids, molecular liquids, liquid crystals, surface phenomena, theory of the dielectric constant, etc. Students who have not taken PHYS 704 but have an equivalent background in Statistical Physics may seek the instructor's consent to register in this course.

Introduction to group theory; symmetry, the group concept, representation theory, character theory. Applications to molecular vibrations, the solid state, quantum mechanics and crystal field theory.

Emphasis on atomic structure and spectroscopy. Review of angular momentum, rotations, Wigner-Eckart theorem, n-j symbols. Energy levels in complex atoms, Hartree-Fock theory, radiative transitions and inner shell processes. Further topics selected with class interest in mind, at least one of which to be taken from current literature.

Angular momentum and the rotation of molecules; introduction to group theory with application to molecular vibrations; principles of molecular spectroscopy; spectra of isolated molecules; intermolecular interactions and their effects on molecular spectra; selected additional topics (e.g., electronic structure of molecules, experimental spectroscopic techniques, neutron scattering, correlation functions, collision induced absorption, extension of group theory to molecular crystals, normal coordinate analysis, etc.).

Static properties of nuclei; alpha, beta, gamma-decay; two-body systems; nuclear forces; nuclear reactions; single-particle models for spherical and deformed nuclei; shell, collective, interacting boson models.

Strong, electromagnetic and weak interactions. Isospin, strangeness, conservation laws and symmetry principles. Leptons, hadrons, quarks and their classification, formation, interactions and decay.

Physical properties of atomic liquids; distribution functions and equilibrium properties, elementary perturbation theories and integral equation theories; simple metals, simple computer simulation; viral expansions and thermodynamic derivatives of g(r); experimental determination of g(r).

Transport properties; optical properties; magnetism; superconductivity; disordered systems.

Offered on demand. Course content depends on topic and instructor.

A modern approach to the quantum many-body problem from the perspective of condensed matter physics. Low energy effective theories, continuum field theories, and lattice models. Phases and phase transitions in the path integral formulation of bosons, fermions and quantum spins. Quantum critical points, topological phases, gauge theories, and connections to quantum information.

Optoelectronic component fabrication, light propagation in linear and nonlinear media, optical fiber properties, electro-optic and acousto-optic modulation, spontaneous and stimulated emission, semiconductor lasers and detectors, noise effects in fiber systems.

This course provides an overview of the application of physics to medicine. The physical concepts underlying the diagnosis and treatment of disease will be explored. Topics will include general imaging principles such as resolution, intensity and contrast; x-ray imaging and computed tomography; radioisotopes and nuclear medicine, SPECT and PET; magnetic resonance imaging; ultrasound imaging and radiation therapy.

Review of basics of quantum information and computational complexity; Simple quantum algorithms; Quantum Fourier transform and Shor factoring algorithm: Amplitude amplification, Grover search algorithm and its optimality; Completely positive trace-preserving maps and Kraus representation; Non-locality and communication complexity; Physical realizations of quantum computation: requirements and examples; Quantum error-correction, including CSS codes, and elements of fault-tolerant computation; Quantum cryptography; Security proofs of quantum key distribution protocols; Quantum proof systems. Familiarity with theoretical computer science or quantum mechanics will also be an asset, though most students will not be familiar with both.

Offered on demand. Course content depends on topic and instructor.

Offered on demand. Course content depends on topic and instructor.

Multi-wavelength astronomy: radio, infrared, optical and x-ray observations. Radiative Processes: macroscopic description, thermal and non-thermal emission, scattering, line transitions and plasma effects. Gravitational Dynamics: potential and orbits, self-gravitating systems, the Collisionless Boltzmann Equation, gravitational encounters. Fluid Mechanics: simple fluids, soundwaves and shocks, instabilities and transport mechanisms.

Review of elementary general relativity. Timelike and null geodesic congruences. Hypersurfaces and junction conditions. Lagrangian and Hamiltonian formulations of general relativity. Mass and angular momentum of a gravitating body. The laws of black-hole mechanics.

Introduction to the differential geometry of Lorentzian manifolds. The priniciples of general relativity. Causal structure and cosmological singularities. Cosmological space-times with Killing vector fields. Friedmann-Lemaitre cosmologies, scalar, vector and tensor perburbations in the linear and nonlinear regimes. De Sitter space-times and inflationary models.

Offered on demand. Course content depends on topic and instructor.