# IX. Graduate Programs

## Physics

### Courses

* Courses offered annually. Other courses are offered on an alternate year basis and as requested.

#### Perimeter Scholars' Institute Courses

PHYS*6010 PSI Quantum Field Theory I U [0.50] | |
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Canonical quantization of fields, perturbation theory, derivation of Feynman diagrams, applications in particle and condensed matter theory, renormalization in phi^4. | |

Department(s): | Department of Physics |

PHYS*6020 PSI Statistical Physics U [0.50] | |
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A brief review of ensembles and quantum gases, lsing model, landau theory of phase transititions, order parameters, topology, classical solutions. | |

Department(s): | Department of Physics |

PHYS*6030 PSI Quantum Field Theory II U [0.50] | |
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Feynman Path Integral, abelian and nonabelian guage theories and their quantization, spontaneous symmetry breaking, nonperturbative techniques: lattice field theory, Wilsonian renormalization. | |

Department(s): | Department of Physics |

PHYS*6040 PSI Relativity U [0.50] | |
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Special relativity, foundations of general relativity, Riemannain geometry, Einstein's equations, FRW and Schwarzschild geometries and their properties. | |

Department(s): | Department of Physics |

PHYS*6050 PSI Quantum Theory U [0.50] | |
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Schrodinger equation: free particle, harmonic oscillator, simple time-dependent problems, Heisenberg picture and connection with classical physics. Entanglement and non-locality. Pure and mixed states, quantum correlators, measurement theory and interpretation. | |

Department(s): | Department of Physics |

PHYS*6060 PSI Information and Data Analysis U [0.50] | |
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Probability, entropy, Bayesian inference and information theory. Maximum likelihood methods, common probability distributions, applications to real data including Monte Carlo methods. | |

Department(s): | Department of Physics |

PHYS*6070 PSI Dynamical Systems U [0.50] | |
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Maps, flows, stability, fixed points, attractors, chaos, bifurcations, ergodicity, approach to chaos. Hamiltonian systems, Liouville, measure, Poincare theorem, integrable systems with examples. | |

Department(s): | Department of Physics |

PHYS*6080 PSI Computation U [0.50] | |
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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 programing. | |

Department(s): | Department of Physics |

PHYS*6210 PSI Cosmology U [0.25] | |
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FRW metic, 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 anisopropies, inlation and observational tests. | |

Department(s): | Department of Physics |

PHYS*6220 PSI Standard Model U [0.25] | |
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Application of Yan-Mills theory to particle physics, QCD and its tests in the perturbative regime, theory of weak interactions, precisions tests of electroweak theory, CKM matrix and flavour physics, open questions. | |

Department(s): | Department of Physics |

PHYS*6230 PSI String Theory U [0.25] | |
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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- 11-dimensional supergravities. Simple supergravity solutions and use these to explore some aspects of adS/CFT duality. | |

Department(s): | Department of Physics |

PHYS*6240 PSI Mathematical Physics Topics U [0.25] | |
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Differential forms, de Rham cohomology, differential topology and characteristic classes, monopoles and instantons, Kahler manifolds, Dirac equations, zero modes and index theorems. | |

Department(s): | Department of Physics |

PHYS*6350 PSI Quantum Information Review U [0.25] | |
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Review of selected topics in Quantum Information. | |

Department(s): | Department of Physics |

PHYS*6360 PSI Gravitational Physics Review U [0.25] | |
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Review of selected topics in Gravitational Physics. | |

Department(s): | Department of Physics |

PHYS*6370 PSI Condensed Matter Theory U [0.25] | |
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Review of selected topics in Condensed Matter Theory. | |

Department(s): | Department of Physics |

PHYS*6380 PSI Quantum Gravity U [0.25] | |
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Review of selected topics in Quantum Grativity. | |

Department(s): | Department of Physics |

PHYS*6390 PSI Foundations of Quantum Theory U [0.25] | |
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Review of selected topics in Foundations of Quantum Theory. | |

Department(s): | Department of Physics |

PHYS*6410 PSI Explorations in Quantum Information U [0.25] | |
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Review of selected topics in Quantum Information. | |

Department(s): | Department of Physics |

PHYS*6420 PSI Explorations in Gravitational Physics U [0.25] | |
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Review of selected topics in Gravitational Physics. | |

Department(s): | Department of Physics |

PHYS*6430 PSI Exploration in Condensed Matter Theory U [0.25] | |
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Review of selected topics in Condensed Matter Theory. | |

Department(s): | Department of Physics |

PHYS*6440 PSI Exploration in Quantum Gravity U [0.25] | |
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Review of selected topics in Quantum Gravity. | |

Department(s): | Department of Physics |

PHYS*6450 PSI Explorations in Foundations of Quantum Theory U [0.25] | |
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Review of selected topics in Foundations of Quantum Theory. | |

Department(s): | Department of Physics |

PHYS*6460 PSI Explorations in Particle Physics U [0.25] | |
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Review of selected topics in Particle Physics. | |

Department(s): | Department of Physics |

PHYS*6470 PSI Explorations in String Theory U [0.25] | |
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Review of selected topics in String Theory. | |

Department(s): | Department of Physics |

PHYS*6480 PSI Explorations in Complex Systems U [0.25] | |
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Review of selected topics in Complex Systems. | |

Department(s): | Department of Physics |

PHYS*6490 PSI Explorations in Cosmology U [0.25] | |
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Review of selected topics in Cosmology. | |

Department(s): | Department of Physics |

#### Basic Group

PHYS*7010 Quantum Mechanics I * U [0.50] | |
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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. | |

Department(s): | Department of Physics |

PHYS*7020 Quantum Mechanics II U [0.50] | |
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Concepts of relativistic quantum mechanics, elementary quantum field theory, and Feynman diagrams. Application to many-particle systems. | |

Prerequisite(s): | PHYS*7010 or equivalent |

Department(s): | Department of Physics |

PHYS*7040 Statistical Physics I* U [0.50] | |
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Statistical basis of thermodynamics; microcanonical, canonical and grand canonical ensembles; quantum statistical mechanics, theory of the density matrix; fluctuations, noise, irreversible thermodynamics; transport theory; application to gases, liquids, solids. | |

Department(s): | Department of Physics |

PHYS*7050 Statistical Physics II U [0.50] | |
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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. | |

Prerequisite(s): | PHYS*7040 or equivalent. |

Department(s): | Department of Physics |

PHYS*7060 Electromagnetic Theory * U [0.50] | |
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Solutions to Maxwell's equations; radiation theory, normal modes; multipole expansion; Kirchhoff's diffraction theory; radiating point charge; optical theorem. Special relativity; transformation laws for the electromagnetic field; line broadening. Dispersion; Kramers-Kronig relations. Magnetohydrodynamics and plasmas. | |

Department(s): | Department of Physics |

PHYS*7080 Applications of Group Theory U [0.50] | |
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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. | |

Department(s): | Department of Physics |

PHYS*7670 Introduction to Quantum Information Processing F [0.50] | |
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Quantum superposition, interference, and entanglement. Postulates of Quantum Mechanics. Quantum computational complexity. Quantum Algorithms. Quantum communication and cryptography. Quantum error correction. Implementations. | |

Department(s): | Department of Physics |

#### Subatomic and Nuclear

PHYS*7030 Quantum Field Theory U [0.50] | |
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Review of relativistic quantum mechanics and classical field theory. Quantization of free quantum fields (the particle interpretation of field quants). 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. | |

Prerequisite(s): | PHYS*7010 or equivalent. |

Department(s): | Department of Physics |

PHYS*7090 Green's Function Method U [0.50] | |
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Review of essential quantum field theory. Zero and finite temperature. Green's functions. Applications. | |

Department(s): | Department of Physics |

PHYS*7150 Nuclear Physics U [0.50] | |
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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. | |

Department(s): | Department of Physics |

PHYS*7160 Special Topics in Subatomic and Nuclear Physics U [0.50] | |
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Restriction(s): | Instructor consent required. |

Department(s): | Department of Physics |

PHYS*7170 Intermediate and High Energy Physics U [0.50] | |
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Strong, electromagnetic and weak interactions. Isospin, strangeness, conservation laws and symmetry principles. Leptons, hadrons, quarks and their classification, formation, interactions and decay. | |

Department(s): | Department of Physics |

PHYS*7180 Special Topics in Subatomic and Nuclear Physics U [0.25] | |
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Restriction(s): | Instructor consent required. |

Department(s): | Department of Physics |

#### Astronomy and Astrophysics

PHYS*7810 Fundamentals of Astrophysics U [0.50] | |
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The fundamental astronomical data: techniques to obtain it and the shortcomings present. The classification systems. Wide- and narrow-band photometric systems. The intrinsic properties of stars: colours, luminosities, masses, radii, temperatures. Variable stars. Distance indicators. Interstellar reddening. Related topics. | |

Department(s): | Department of Physics |

PHYS*7840 Advanced General Relativity W [0.50] | |
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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. | |

Department(s): | Department of Physics |

PHYS*7850 Quantum Field Theory for Cosmology U [0.50] | |
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Introduction to scalar field theory and its canonical quantization in flat and curved spacetimes. The flat space effects of Casimir and Unruh. Quantum fluctuations of scalar fields and of the metric on curved space-times and application to inflationary cosmology. Hawking radiation. | |

Prerequisite(s): | PHYS*7010 |

Department(s): | Department of Physics |

PHYS*7860 General Relativity for Cosmology U [0.50] | |
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Introduction to the differential geometry of Lorentzian manifolds. The principles of general relativity. Causal structure and cosmological singularities. Cosmological space-times with Killing vector fields. Friedmann-Lemaitre cosmologies, scalar vector and tensor perturbations in the linear and nonlinear regimes. De Sitter space-times and inflationary models. | |

Department(s): | Department of Physics |

PHYS*7870 Cosmology U [0.50] | |
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Friedmann-Robertson-Walker metric and dynamics; big bang thermodynamics; nucelosynthesis; recombination; perturbation theory and structure formation; anisotropies in the Cosmic Microwave Background; statistics of cosmological density and velocity fields; galaxy formation; inflation. | |

Department(s): | Department of Physics |

PHYS*7880 Special Topics in Astronomy U [0.50] | |
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Offered on demand | |

Department(s): | Department of Physics |

PHYS*7890 Special Topics in Astrophysics U [0.25] | |
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Offered on demand | |

Department(s): | Department of Physics |

PHYS*7900 Special Topics in Gravitation and Cosmology U [0.50] | |
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Department(s): | Department of Physics |

PHYS*7910 Special Topics in Gravitation and Cosmology U [0.25] | |
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Department(s): | Department of Physics |

#### Atomic and Molecular

PHYS*7100 Atomic Physics U [0.50] | |
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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 is to be taken from current literature. | |

Department(s): | Department of Physics |

PHYS*7130 Molecular Physics U [0.50] | |
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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 co-ordinate analysis, etc.). | |

Department(s): | Department of Physics |

#### Condensed Matter

PHYS*7310 Solid State Physics I U [0.50] | |
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Phonons, electron states, electron-electron interaction, electron-ion interaction, static properties of solids. | |

Department(s): | Department of Physics |

PHYS*7320 Solid State Physics II U [0.50] | |
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Transport properties; optical properties; magnetism; superconductivity; disordered systems. | |

Department(s): | Department of Physics |

PHYS*7330 Special Topics in Theoretical Condensed Matter Physics U [0.50] | |
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Department(s): | Department of Physics |

PHYS*7370 Special Topics in Surface Physics U [0.50] | |
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Department(s): | Department of Physics |

#### Biophysics

PHYS*7510 Clinical Applications of Physics in Medicine U [0.50] | |
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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. Offered in conjunction with PHYS*4070. Extra work is required of graduate students. | |

Restriction(s): | Credit may be obtained for only one of PHYS*4070 or PHYS*7510. |

Department(s): | Department of Physics |

PHYS*7520 Molecular Biophysics U [0.50] | |
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Physical methods of determining macromolecular structure: energetics, intramolecular and intermolecular forces, with application to lamellar structures, information storage, DNA and RNA, recognition and rejection of foreign molecules. Offered in conjunction with PHYS*4540. Extra work is required of graduate students. | |

Restriction(s): | Credit may be obtained for only one of PHYS*4540 or PHYS*7520 |

Department(s): | Department of Physics |

PHYS*7540 Special Topics in Biophysics U [0.50] | |
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Offered on demand | |

Department(s): | Department of Physics |

PHYS*7570 Special Topics in Biophysics U [0.25] | |
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Offered on demand | |

Department(s): | Department of Physics |

#### Applied Physics (including Technical Methods)

PHYS*7140 Nonlinear Optics U [0.50] | |
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Classical and Quantum Mechanical descriptions of nonlinear susceptibility, nonlinear wave propogation, nonlinear effects such as Peckel's and Kerr effects, harmonic generation, phase conjugation and stimulated scattering processes. | |

Department(s): | Department of Physics |

PHYS*7450 Special Topics in Experimental Physics * U [0.50] | |
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A modular course in which each module deals with an established technique of experimental physics. Four modules will be offered during the Winter and Spring semesters, but registration and credit will be in the spring semester. Typical topics are neutron diffraction, light scattering, acoustics, molecular beams, NMR, surface analysis, etc. | |

Department(s): | Department of Physics |

PHYS*7470 Optical Electronics U [0.50] | |
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Optoelectronic component fabrication, light propogation in linear and nonlinear media, optical fiber properties, electro-optic and acousto-optic modulation, spontaneous and stimulated emission, semiconductor lasers and detectors, nose effects in fiber systems. | |

Department(s): | Department of Physics |

#### Special Courses (offered on demand only)

PHYS*7120 Special Topics in Theoretical Physics U [0.50] | |
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Department(s): | Department of Physics |

PHYS*7710 Special Lecture and Reading Course U [0.50] | |
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Department(s): | Department of Physics |

PHYS*7730 Special Topics in Physics U [0.50] | |
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Department(s): | Department of Physics |

PHYS*7750 Interinstitution Exchange U [0.50] | |
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At the GWPI director's discretion, a PhD or MSc student may receive credit for a term of specialized studies at another institution. Formal evaluation is required. | |

Restriction(s): | GWPI director approval required |

Department(s): | Department of Physics |

PHYS*7970 MSc Project U [1.00] | |
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Study of a selected topic in physics presented in the form of a written report. For students whose MSc program consists entirely of courses | |

Department(s): | Department of Physics |