Physics 619   Fields II    (Fall 2016) 

Course info      |     Plan of lectures   |  Homeworks and Solutions     |     Useful Links      |     E-mail

Course info

Room: SEC-217
           Monday,    10:20-11:40 AM
           Thursday;   10:20-11:40 AM

Instructor: Sergei Lukyanov
         office: Serin E364
         office phone: (848) 445-9060 
         e-mail: sergei@physics.rutgers.edu (the best way)

Office hours: Wednesday 2:00-4:00 pm



Text Books: 1) M.E. Peskin, D.V. Schroeder: An Introduction to Quantum Field
                    Theory,
   Westview Press, 1995;
                   2) M. Srednicki: Quantum Field Theory
                   PDF notes version (similar to the published version) can be found at
                   http://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf

Homework: There will be homework assignments.
                        Late homework will not be accepted. Homeworks will be graded and give
                        100% contribution to your final grade
Exams: There will be no exams.

Students with Disabilities:

If you have a disability, it is essential that you speak to the course supervisor early in the semester to make the necessary arrangements to support a successful learning experience. Also, you must arrange for the course supervisor to receive a Letter of Accommodation from the Office of Disability Services.
http://www.physics.rutgers.edu/ugrad/disabilities.html

Download this info in PDF format

 

Prerequisites  

This course is a continuation of 618 (Fields I). At Spring you have used Srednicki's textbook. It was covered almost all of Part I (spin 0), and most of Part II (spin 1/2). Specifically, in Part II chapters 34-37, 39, 40, 42-45, 48, 51, 52. There were also couple of lectures on critical phenomena, the Ising model and phi^4 theory which is not in Srednicki's book.
    If you did not take Fields I, it is your responsibility to do background reading to make sure you understand the concepts in this course. Specifically, I will assume that you are familiar with the following concepts:

  •   Canonical quantization of scalar and spin-1/2 fields   (M. Peskin, D. Schroeder: Chs. 2,3)
  •   Renormalized perturbation theory   (phi^4 and Yukawa theories)
          (PS: Chs. 4.1-4.4, 4.7, 10.1-10.2)
  •   Path-integral quantization of scalar and spin-1/2 fields
          (both Minkowski and Euclidian forms) (PS: Chs. 9.1-9.3, 9.5)
  •   Renormalization Group (PS: Chs. 12.1-12.3)
  •   General form of the spectrum in QFT, S-matrix, LSZ formalism
          (PS: Chs. 4.5, 4.6, 7.1-7.3)
  •   Spontaneous Symmetry Breaking (PS: Ch. 11.1)

     

  • Plan of  lectures

    This is a tentative schedule of what we will cover in the course. It is subject to change, often without notice. These will occur in response to the speed with which we cover material, individual class interests, and possible changes in the topics covered. Use this plan to read ahead from the text books, so you are better equipped to ask questions in class.
     

     

     

                                   QUANTIZATION  OF  EM  FIELD


    •  Canonical quantization:    General aspects of quantization of systems with constraints. Brief overview of the Lorentz group. Maxwell's equations. EM field as a dynamical system with constraints. Quantization in the Coulomb gauge.
      Literature: 1) M. Srednicki: Quantum Field Theory (Chapters 33, 54-56)
    •   Covariant path integral quantization:    Euclidean path integral. Gauge group. Gauge fixing conditions. Faddeev-Popov trick. Feynman propagator.
      Literature: 1) M.E. Peskin, D.V. Schroeder: Quantum Field Theory (Chapter 9.4)

                                                                              

                          QUANTUM  ELECTRODYNAMICS


    •   Lagrangian and Feynman rules:    Feynman rules for QED. Gauge invariance of the scattering amplitudes. Electron vertex function (formal structure).
      Literature: 1) M. Srednicki: Quantum Field Theory (Chapters 58-59);
    • 2) M.E. Peskin, D.V. Schroeder: Quantum Field Theory (Chapters 4.7, 5.1, 6.2)
    •   One-loop radiative corrections:   
      Electron propagator. Electron vertex function. Ward-Takahashi identity. Magnetic moment of the electron. Infrared divergence.
      Literature: 1) M.E. Peskin, D.V. Schroeder: Quantum Field Theory (Chapters 6.3-6.5, 7.1, 10.3);
    • 2) M. Srednicki: Quantum Field Theory (Chapters 62-64, 67)
    •   Renormalized Perturbation Theory:     Vacuum polarization: formal structure. Renormalized action and counterterms. Pauli-Villars and dimensional regularizations. Vacuum polarization: evaluation.
      Literature: 1) M.E. Peskin, D.V. Schroeder: Quantum Field Theory (Chapters 10.1, 10.3);
    • 2) M. Srednicki: Quantum Field Theory (Chapter 62)
    •   Renormalization group in QED:   
      Radiative corrections to the Coulomb law. Callan-Symanzik equation. Beta-function.
      Literature: 1) M.E. Peskin, D.V. Schroeder: Quantum Field Theory (Chapters 10.3, 12.3);
    • 2) M. Srednicki: Quantum Field Theory (Chapter 66)

                                                                              

                          NON-ABELIAN   GAUGE   THEORIES


    •   Gauge invariance:    
      Geometry of gauge invariance. Wilson loop. Yang-Mills Lagrangian. Basic facts about Lie algebras. Yang-Mills for an arbitrary compact group.
      Literature: 1) M.E. Peskin, D.V. Schroeder: Quantum Field Theory (Chapters 15.1-15.4);
    • 2) M. Srednicki: Quantum Field Theory (Chapter 69, 70)
    •   Quantization of non-Abelian gauge theories:    
      Path integral quantization. Feynman rules. Ghosts and unitarity. BRST symmetry.
      Literature: 1) M.E. Peskin, D.V. Schroeder: Quantum Field Theory (Chapters 16.1-16.3);
    • 2) M. Srednicki: Quantum Field Theory (Chapters 71, 72, 74)
    •   Asymptotic freedom:    
      Renormalization in the Y-M theory. One-loop divergencies. $\beta$-function. Quantum Chromodyanamics. Background field method. Functional determinants. Seley coefficients.
      Literature: 1) M.E. Peskin, D.V. Schroeder: Quantum Field Theory (Chapters 16.5-16.7, 17.1-17.2);
    • 2) M. Srednicki: Quantum Field Theory (Chapters 73, 78)

                                                                              

                          AXIAL  CURRENTS  IN  GAUGE  THEORIES


    •   Axial current in two dimensions:
      Literature: 1) M.E. Peskin, D.V. Schroeder: Quantum Field Theory (Chapter 19.1)
    •   Bosonization in two dimensions:   Schwinger model
    •   Axial current in four dimensions:
      Literature: 1) M.E. Peskin, D.V. Schroeder: Quantum Field Theory (Chapters 19.2);
    • 2) M. Srednicki: Quantum Field Theory (Chapter 73, 76, 77)
    •   Goldstone bosons and chiral symmetries in QCD  
      Literature: 1) M.E. Peskin, D.V. Schroeder: Quantum Field Theory (Chapter 19.3);
    • 2) M. Srednicki: Quantum Field Theory (Chapter 83)

                                                                              

                          GAUGE  THEORIES   WITH SPONTAEOUS
                    SYMMETRY  BREAKING


    •   Higgs mechanism;  
      Literature: 1) M.E. Peskin, D.V. Schroeder: Quantum Field Theory (Chapter 20.1);
    • 2) M. Srednicki: Quantum Field Theory (Chapter 84)
    •   Quantization of spontaneously broken gauge theories;  
      Literature: 1) M.E. Peskin, D.V. Schroeder: Quantum Field Theory (Chapter 20.1);
    • 2) M. Srednicki: Quantum Field Theory (Chapters 85, 86)
    •   Glashow-Weinberg-Salam theory of weak interactions;  
      Literature: 1) M.E. Peskin, D.V. Schroeder: Quantum Field Theory (Chapters 20.2);
    • 2) M. Srednicki: Quantum Field Theory (Chapters 87-89)

    Download syllabus

     

    Homeworks and Solutions  

    The assignments and solutions are stored in PDF format. The absolute cutoff time for homework is 4pm due date.


    Assigned on
    Assignment
    Due Date
    Solution
     
    1. Sep 8, 2016 pdf   Sep 29, 2016 pdf  
    2. Sep 26, 2016 pdf   Oct 13, 2016 pdf  
    3. Oct 13, 2016 pdf   Nov 10, 2014 pdf  
    4. Nov 7, 2016 pdf   Nov 28, 2016 pdf  
    5. Nov 21, 2016 pdf   Dec 12, 2016 pdf  
    6. Dec , 2016 pdf   Dec , 2016 pdf  
    Useful Links  
    1. "Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables",
    M. Abramowitz and I. Stegun
       
       

    Course info     |     Plan of lectures  |     Homeworks and Solutions     |     Useful Links     |     E-mail