Fundamentals of Quantum Field Theory

  Teacher:  Professor You-Quan Li

Schedule 2001 (place): Tuesday 1-2; Wednesday 3-4(Room 404 in Building No.9); Friday 1-2 (ZIMP, Room 203)

     The main purpose of this course is to provide for advanced undergraduate students or graduate students who have no prior knowledge of quantum field theory, but familiar with special relativity and quantum mechanics. The teacher will attempt to avoid heavy mathematical formulation as much as possible by introducing the basic machinery of Feynman diagrams through decay processes even before dealing with the quantisation of vector fields. Whereas, the students are highly suggested to make notes in the class so that they can follow the necessary formulations by themselves and carry out the exercises that the teacher feels the student would benefit most.

     As long as the students have a better understanding of this fundamental course, they will have no difficult to take advanced courses for special research interests further. Such as Quantum field theory in condensed matter physics, Quantum field theory in high- energy physics, or Quantum Yang-Mills field theory.

Online References:

Wilczek,  

       QCD Made Simple (如无法访问国外网，点击这里)

H.Kleinert,

       Gauge theory in condensed matter physics 

Zhao Guang-Da

      Lecture of quantum field theory

Reference text books

M. Stone, 《The Physics of Quantum Field Theory》

K. Huang,《Quantum Field Theory-from operaotr to path integraals》

M.E. Peskin and D.V. Schroeder,《An Introduction to Quantum Field Theory 》

S.J.Chang,《Introduction to Quantum Field Theory》

C. Itzykson and J. Zuber, 《Quantum Field Theory》 Vol. 1
(there are Chinese translations in the Library)

D. Lurie, 《Particles and Field》 Chapter 1- 7
(there are Chinese translations in the Library)

W. Greiner.Joachim Reinhardt, 《Field Quantization》
G. Sterman, 《an introduction to QUANTUM FIELD THEORY 》 part I-II

N.N. Bogoliubov and D.V. Shirkov, 《Quantum Field》 Chapter I-V

Tentative contents

Part I:  Introduction

1. History survey  

2. Elementary particles and fundamental interactions

3. Relativistic quantum mechanics

one question , two excises

Part II:  Classical Field Theory

1. natural units
2. general Lorentz transformation
3. Covariant form of scalar and vector field equations
4. Euler-Lagrange equatioin in field theory
5. Hamiltonian formulation
6. Neother's theorem

7. Energy-Momentum tensor
8. Global symmetry and charge conservation.

three excises:

Part III:  Quantization of scalar fields

1. Revisit of quantization in quantum mechanics
2. The field and its canonical quantization
3. Ground state of the Hamiltonian and normal ordering
4. Fock space
6. Complex scalar field
7. Creation and annihilation operators
8. Particle and antiparticles
9. Fourier decomposition of the field
10.Heisenberg picture and Heisenberg equation
11.Reformulate the commutation relations 
12. Propagator

three excises:

Part IV:  Quantization of the electromagnetic filed   

           1. Fock space representation  
           2. Gauge condition (Gupta weak condition)
           3. Polarization of photons
           4. Propagator 

          one excises:

Part V:  Quantization of the Dirac field    

      C-1 Gamma matrices 
      C-2.Covariant form of Dirac equation   
      C-3.Plane wave solution of Dirac equation Positive  and negative energy spinors 4. 
      C-4.Spinor representation of Lorentz group
      C-5.Conjugation equation of Dirac field  
      C-6.Vectors and tensors involving gamma matrices
      Q-1.Occupation number representation of bosons and fermions  
      Q-2.Fourier decomposition of Dirac field 
      Q-3.Fermionic  Fock space 
      Q-4.Green function and Feymann function 
             four excises:

Part VI:  The S-matrix expansion and   Feynman diagrams 

       1. Interactions of Fields  
       2. Evolution operator   
       3. S-matrix 
       4. Wick's theorem     
       5. The S-matrix expansion of QED interaction.   
       6.  Feynman rules and Feynman diagrams  
           three excises:

Part VII:  Cross sections and decay rates

       1. Definition of cross section   
       2. Rutherfold scattering
       3. Compton scattering
       4. mu-decay     
           one or two big  excises:  

Part VIII: Parity, Time reversal and Charge conjugation.

       1. Charge conjugation transformation 
       2. Wigner time reversal 
       3. CP transformation and CPT theorem 
          three or two excises:  

* Part IX: A short description of renormalization concept  in  quantum electrodynamics   
           zero excises