Winter 1996

ADVANCED QUANTUM MECHANICS

(Physics 235B)

The first quarter of Advanced Quantum Mechanics (235A) is a pre-requisite for 235B. The following is a rough outline of the course.

Path Integral Quantization. Harmonic Oscillator. N degrees of freedom. Vacuum Expectation Values. Fermions. Generating Functional of Free and Interacting Green’s Functions. Exact Two-Point Function in Perturbation Theory. Relation to Ising Model.

Self-Interacting Scalar Theory. Cancellation of Vacuum Diagrams. Four-Point Function to Second Order. Divergences, Ultraviolet Cutoff and Renormalization. Scale Dependence of the Coupling. Beta Function. O(n) Invariant Scalar Theory. Superficial Degree of Divergence and Perturbatively Renormalizable Theories.

Gauge Theories. Quantum Electrodynamics. Electron Self-Energy. Photon Self-Energy. Vertex Correction. Lie Groups. Generators and Representations. SU(n) Group. Non-Abelian Gauge Theories. Covariant Derivative. Yang-Mills Lagrangian. Wilson Loop.

Spontanous Symmetry Breaking. Goldstone Theorem. Higgs Mechanism in The Abelian and Non-Abelian Case. Glashow-Weinberg-Salam Model. Weak Angle and W/Z Masses. Higgs Particle. Trviality Bound on Higgs Mass. Quantum Chromodynamics.

Quantization of Gauge Theories. Zero Modes and Gauge Conditons. Fadeev-Popov Determinant. Ghost Fields. Feynman Rules. Renormalization Constants. Renormalization Group and Callan-Symanzik Equations.

Higher Order Corrections. Fermion Self-Energy. Dimensional Regularization. Gluon Self-Energy. Ghost Loop. Vertex Corrections. Running Gauge Coupling. Asymptotic Freedom. QED in dimensional Regularization. e+e- into Hadrons. Quark Confinement. Wilson Loop in Perturbation Theory. Lattice Gauge Theory. Supersymmetry. Gravity as a Gauge Theory. Finite Temperature Field Theory.

Recommended Books:

Quantum Field Theory, by C. Itzykson and J-B Zuber, (McGraw-Hill, 1980).

Introduction to Quantum Field Theory, by L. Ryder (Cambridge University {Press, 1985).

Field Theory: A Moder Primer, by P. Ramond (Benjamin Cummings, 1990).

An Introduction Quantum Field Theory, by M.E. Peskin and D.V. Schroeder, (Addison Wesley 1995).

Herbert W. Hamber, FRH 3172 hhamber@uci.edu