Phys 961: Quantum Field Theory I                                                                                                                                                         peskin                                     
 


 Spring 2005
 
T TH 11:10-12:30,   DEM 304                                                                                                                                                                                                                                     

Instructor:   Silas Beane

Office:    DEM 209E                   Phone:   603-862-2720

email:   silas@physics.unh.edu      web:   http://www.physics.unh.edu/~silas                                                                                                                                                                                                                      
Office hours:   Tuesday and Thursday afternoons



Course information

Textbook

The main textbook for this course is An Introduction to Quantum Field Theory by Peskin and Schroeder (see picture above).

Email and Office Hours

I strongly encourage students to communicate with me by email for bureaucratic issues. At times, I'll communicate with the class by email.
Please, no physics questions via email!

If necessary, you may visit me outside of office hours but please do not be offended if I'm unable to speak with you immediately.

Homeworks, Exams and Grades

The grade for this course will be based on a midterm homework (50%) and a final homework (50%). There will be no exams.

Topics Covered in QFT I and QFT II

Bosonic Fields:  
second quantization of bosons; 
non-relativistic quantum fields;
relativistic free particles and the Klein-Gordon field;
causality and the Klein-Gordon propagator;
quantum electromagnetic fields and photons.
Fermionic Fields:
second quantization of fermions;
Dirac equation and its non-relativistic limit;
quantum Dirac field;
spin-statistics theorem;
Dirac matrix techniques;
Lorentz and discrete symmetries.

Interacting Fields and Feynman Rules:
perturbation theory;
correlation functions;
Feynman diagrams;
S-matrix and cross-sections;
Feynman rules for fermions;
Feynman rules for QED.

Functional Methods:
path integrals in quantum mechanics;
path integrals for classical fields and functional quantization;
functional quantization of QED;
QFT and statistical mechanics;
symmetries and conservation laws.

Quantum Electrodynamics:
some elementary processes;
radiative corrections;
infrared and ultraviolet divergences;
renormalization of fields and of the electric charge;
Ward identities.

Renormalization Theory:
systematics of renormalization;
integrating out and the Wilsonian renormalization group;
running of the coupling constants and the renormalization group.

Non-Abelian Gauge Theories:
non-abelian gauge symmetries;
Yang-Mills theory;
interactions of gauge bosons and Feynman rules;
Fadde'ev-Popov ghosts and BRST;
renormalization of YM theories and asymptotic freedom;
the Standard Model.


Some useful texts (on reserve in the library)
 
1) Quantum Field Theory in a Nutshell
by A.Zee

2) Quantum Field Theory
by L.Ryder

3) Quantum Field Theory V1 and V2
by S.Weinberg

4) Field Theory: A Modern Primer
by P.Ramond

5) Quantum Field Theory
by C.Itzykson and J.Zuber

6) Gauge Theories in Particle Physics: a Practical Introduction
by I.Aitchison and A.Hey

7) Gauge Field Theories
by S.Pokorski

Calendar  (topics covered & homework)

         Week

                              
  1/18, 1/20                                        
Conventions and Introduction (first class missed due to inexplicable rescheduling of comprehensive exam to class time)
      1/25, 1/27
 Classical theory of the scalar field
Euler-Lagrange and the Klein-Gordon equation
Noether's Theorem
Quantization by S.H.O.s
       2/1, 2/3
 Quantization of the scalar field
Heisenberg representation
Causality
       2/8, 2/10
 Causality (continued)
Retarded propagator
 2/15, 2/16,2/17
 Feynman propagator
Interaction with classical source
Pure Lorentz Transformations
Homogeneous Lorentz group
Poincare group (part 1)
The Dirac representation
       2/22, 2/24
 Weyl spinors
Solutions of the Dirac equation
       3/1, 3/3
 Dirac Bilinears
Quantization of Dirac Field
      3/8, 3/10
Quantization of Dirac Field
Spin and Statistics
Poincare group (part 2)
Wigner's theorem

 Midterm Homework (ps,pdf)
(Due 3/29)

Spring Break
       3/22, 3/24
 Discrete symmetries and the Dirac Field
Parity and Time Reversal
       3/29, 3/31
 Time Reversal (cont)
Interacting field theory
        4/5, 4/7
 Wick's Theorem
(no class Thursday)
        4/12, 4/14
 Feynman diagrams
Combinatorics
Disconnected diagrams
The S-matrix
        4/19, 4/21
 The S-matrix (cont)
Cross-sections and decay rates
The S-matrix from Feynman diagrams
        4/26, 4/28
 The S-matrix from Feynman diagrams (cont)
Fermion contractions and Yukawa theory
The Yukawa potential
Quantum Electrodynamics
 Final Homework (ps,pdf)
(Due 5/18)
         4/3, 4/5
 QED (cont)
e+ e- to \mu+ \mu- cross-section
e+e- to hadrons

The outline above is subject to change as the semester progresses.