Physics 663 Quantum Field Theory II
Home Work:
Problem Set #1 Revised Due Date
Problem Set #2
Problem Set #3
Revised Due Date and Corrected Equations
Problem Set #4 Revised Due Date: 24
November 2008 and Read Chapter 7 in Ryder
Lecture Notes:
I) LSZ Axioms-Introduction Corrected and updated version: 23 September 2008
A)
Heisenberg Pix, in- and out-states
B) in- and out-fields
and the perturbative S-matrix
C) the asymptotic condition and the
Yang-Feldman Equation, Reduction Formulae,
Gell-Mann---Low Expansion for Time Ordered Functions
Part a
Part b
D) The Axioms
Axiom 1
Axiom 2
Axiom 3
Axiom 4
Remarks
II) Green Functions = Time Ordered Functions
A)
Perturbation Theory-Gell-Mann—Low Formula
and Generating Functionals: Z[J]
B) Functional Calculus: derivatives and integrals
1) Scalar functions
2) Grassmann functions
C) Feynman Path Integral Representation for Z[J]
D) Gauge Bosons and Constraints
III)
Global Symmetries
A) Global Space-time Symmetries
B) Global Internal Symmetries
C)
Ward-Takahashi Identity Functional Differential Equations-example
SU(2)XSU(2)
IV) Local Symmetries
A)
Non-Abelian Gauge
Theories
B)
Coulomb Gauge and the Faddeev-Popov (f-p)
Method
C) Faddeev-Popov Ansatz-Intuitive
Approach
D) Coulomb Gauge Revisited
E) General Faddeev-Popov Lagrangian
F) Gauge Ward Identity
G)
Gauge Ward Identity and Becchi-Rouet-Stora (BRS) Invariance
and BRS Transformations
V) Renormalization Theory
A)
Regulation, Renormalization and Counter-terms
B) Renormalization Group Equations
C) Composite Operators
D) Callan-Symanzik Equation
Appendix 1: Faddeev-Popov Ghosts
Appendix 2: Connected Green Functions, One-Particle Irreducible Green Functions and the Effective Action