Ph.D Program In Physics
Course Description and content
PHYS 603 Differential Geometry and Quantum Field Theory
Differential manifolds, tangent space, vector fields, local diffeomorphisms, cotangent space, differential forms, exterior derivative. Differential geometric aspects of Lie groups, Lie algebras, orbit, homogeneous spaces, non-linear – model. Fiber bundles, principal bundles, connections. Yang-Mills gauge theories, applications of differential geometry in gauge.
PHYS 604 Lie Groups and Algebras
Lie groups, Lie algebras, cartan sub-algebra, roots, Dynkin diagrams, classification of simple Lie algebras. Toda equations and their integrability. Higgs fields, self-dual monopoles. Classification of unitary representations of simple Lie groups. Weyl’s character formula.
PHYS 617 Cosmology and Particle Physics
Standard cosmology, Robertson-Walker metric, thermal history of the universe, relativistic thermodynamics, phase transitions. Nucleosynthesis, dark matte, density fluctuations, galaxy formation. Inflation. Cosmic strings. Recent work on cosmological models; super-strings. Recent work on cosmological models; super-strings, super-gravity, Kaluza-Klein.
PHYS 653 Quantum Electrodynamics
Quantization of a free scalar field. Classical e.m. field, gauge transformations. Quantization of the e.m. field, Lorentz gauge, extended Fock space, Green’s functions. Dirac equation. Interaction picture, Perturbation theory, Feynman rules, phase space. The processes eg , em and e+e-. Divergences, regularization and renormalization., General gauges.
PHYS 657 Advanced Quantum Field Theory (3 credit-hours)
Renormalizatin of quantum field theories, normalization conditions, counter-terms, Zero-mass limit, asymptotic behaviour. Functional method in Q.F.T., path integrals, generating functional, effective action, effective potential. The d-model, Renormalization, symmetry breaking, anomalies, Gauge fields, Quantization of gauge fields.
PHYS 658 The Electroweak Model (3 credit-hours)
Gauge theories, symmetry breaking. Standard electroweak model, particle representations, generations, neutral currents, relation to four-fermion theory, particle masses, GIM mechanism, universality. The electroweak interactions. Kobayashi-Maskawa matrix, experimental determination of the parameters. The running coupling constants, implications of the renormalization group equations, grand unification.
PHYS 663 Advanced Particles Physics. (3 credit-hours)
Quark model of hadrons, solutions, bag models. Gluon exchange, mass formulae, quark masses, heavy quarks. Quark-parton model, deep inelastic electron-nucleon scattering, scaling, corrections to scaling behaviour, jets. Chiral symmetry, chiral symmetry breaking, quark masses.
PHYS 664 Quantum Chromodynamics (3 credit-hours)
The colour group, asymptotic freedom, scaling violatius in deep in elastic scattering. Renormalization group – functions. Operator-produce expansions, anomalous dimensions. Non-perturbative QCD, dispersion sum rules. The QCD vacuum, U(1)-problem, confinement; strong CP violation.
PHYS 665 Grand Unification (3 credit-hours)
Review of Lie groups and their representations. The groups SU(5), SO(10) and E6. Unification I the standard model. Georgi-Glashow SU(5) model. Proton decay. Other unification models: SO(10), E6, SU(4) x SU(4). Problems of grand unified models. Future outlook.
PHYS 666 Suprsymmetry. (3 credit-hours)
Two-dimensional superspace, superfield, scalar and vectgor multiplets; N=1/2, N=1, N=2. Four-dimensional superspace, supersymmetry groups, super-integration, expansion, projection operators. Classical N=1, superfield propagators, super . Explicit and spontaneous supersymmetry breaking, super-Higgs.
PHYS 667 String Theory (3 credit hours)
Path integrals, Faddeev-Popov quantization. Free bosonic strings. Quantization; light-cone, BRST. Trees, vertex operators, closed strings. Superstrings, NSR-model, ghosts, extended supersymmetry. String group, tangent space, connections, covariant derivative. Anomalies, Atiyah-Singer theorem.
PHYS 668 Supergravity (3 credit-hours)
Classical N=1 supergravity, covariant approach to supergravity, constraints, actions, Quantum superields, regularization, anomalies, Quantum N=1 supergravity, background splitting, ghosts, Feynman’s rules, dimensional regularization. Supergravity and symmetry breaking.
PHYS 690 Selected Topics in Particle and Field Theory (3 credit-hours)
Covers topical areas in recent research such as lattice gauge theory, finite-temperature field theory, Kac-Moody algebras, phase transitions and critical phenomena.