Fall 1995

ADVANCED QUANTUM MECHANICS

(Physics 235A)

The course is intended as a modern introduction to (mostly Relativistic) Quantum Field Theory. The following is a rough outline of the course.

Scalar Field. Klein-Gordon Equation. Action and Classical Euler-Lagrange Equations. Plane Wave Solutions. Conserved Current. Quantization. Equal Time Commutation Relations. Heisenberg Equations of Motion. Causality and Unequal Time Commutator. Fock Space. Complex Field. Charge Operator. Noether’s Theorem. Isospin. Non-Linear Sigma Model. Parity and Time Reversal. Time Ordering and Feynman Propagator.

Dirac Field. Gamma Matrices. Relativistic Covariance. Plane Wave Solutions. Spin Projection Operators. Weyl Equation. Non-Relativistic Limit. Quantization. Feynman Propagator. Charge Density. Charge Conjugation. Lorentz Transformations on Spinors. Parity and Time Reversal. Classification of Dirac Bilinears. Positronium.

Non-Relativistic Second Quantization. Second Quantized Operators and Observables. Effects of Statistics. Coulomb Interaction.

Quantized Radiation Field. Field Strength Tensor. Construction of the Lagrangian. Canonical Quantization. Gauge Conditions. Photon Polarization States. Photon Propagator. Massive Vector Field. Stueckelberg Lagrangian.

Interacting Fields. Isospin Symmetric Interactions. Scattering Matrix. Reduction Formula. Differential Cross Section. Perturbation Theory. Interaction Picture. Gell-Mann Low Theorem. Wick’s Theorem. Application to Electron Scattering. Feynman Rules. Derivation of Moeller Scattering Formula. Compton Effect. Pair Annihilation. Electron Anomalous Magnetic Moment. Uehling Potential.

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).

Quantum Field Theory and Critical Phenomena, by J. Zinn-Justin (Oxford 1993).

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