June 6, 2000


Physics D15-3   March 28 - June 6 2000 Spring Quarter 2000
TTh 10:30-12:00 in Tech F328 Predrag Cvitanovic'
Course schedule
quantum puppy
They act so cute when they try to understand Quantum Field Theory.

NU Registrar course description
Start: Thursday, March 30, 10:30 in Tech F328.

For people following the course, check the e-mail list.

PROBLEM SETS: Please deliver solutions to problem sets to me, or place them in Yuheng Lan's Physics & Astronomy mailbox (y-lan@nwu.edu).


  1. Feynman's Formulation of Quantum Field Theory
    1. QM Amplitudes as a Sum over Paths
    Suggested reading:
    Peskin: Chap 9 - Functional Methods
    Brown: Chap 1 - Functional integrals (Very clear)

    Exercises, due Tue Apr 18, 2000:
    Fresnel integral: problem 1.14 in Predrag's lecture notes (postscript gzipped) on path integrals
    d-dimensional Gaussian integral: problem 1.15 in Predrag's path integrals lecture notes.
    Greiner & Reinhardt, example 11.2: Weyl ordering for operators
    Greiner & Reinhardt, exercise 11.1: Path integral for a free particle

  2. Schwinger/Feynman Formulation of Field Theory

  3. If you want to relax by listening to diagrammatic, Predragian vision of field theory, I will cover the material in chapters 2-3 of Field Theory in n lectures, n unknown. The exposition assumes no prior knowledge of anything (other than Taylor expansion of an exponential, taking derivatives, and inate knack for doodling). The techniques covered apply to QFT, Stat Mech and stochastic processes.

    Suggested reading:
    Cvitanovic': Field Theory, chapters 2,3
    Peskin: Chap 9 - Functional Methods, sects 9.1, 9.2, 9.3, 9.6
    Peskin: Chap 11 - The Effective Action, sects 11.3, 11.4, 11.5
    Cvitanovic': Field Theory, chapter 4: Fermions

    Exercises, due Tue Apr 25, 2000:
    Predrag's Field Theory exercises 2.D.1, 2.D.2, 2.D.3, 2.E.3, 2.F.1

    Exercises, due Tue May 2, 2000:
    Predrag's Field Theory exercises 3.B.1, 3.F.2

    Exercises, due Tue May 9, 2000:
    Predrag's chapter 4 exercises 4.E.2, 4.F.1

  4. Renormalization

  5. Suggested reading:
    Predrag's Chapt. 5; pp. 66-70; Chapt. 6; p. 71 , Chapt. 6; p. 72-100
    Peskin: Sect 7.2 - LSZ reduction, 7.4 Ward-Takahashi indentities
    Greiner & Reinhardt, Sect 6.4: Vector fields
    Peskin: Chap 10 - Systematics of Renormalization

    Exercise, due Tue May 16, 2000:
    Predrag's chapter 6 exercise 6.A.1: QED Ward identity

    No class May 16, 18 and 23.

    Assignments for period of May 16-23:

    Predrag's exercises 6.E.1, 6.F.2 due Thu May 18, 2000, Y. Lan's mailbox.
    Work through sections 6.G, 6.H and 6.I

    Midterm exam (takehome - including solutions)         Due Thursday, May 25, 2000, 10:30
    Overal course grade will be determined from the homework (40%), midterm (20%), and the final (40%).

  6. Non-Abelian Gauge Invariance
    Suggested reading:
    Peskin: Chap 15 - Non-Abelian Gauge Invariance

  7. Quantization of Non-Abelian Gauge Theories
    Suggested reading:
    Peskin: Sects 16.1-16.4 - Quantization of Non-Abelian Gauge Theories,

    Final exam: takehome, start May 30.

    Required: perform all calculations outlined in Peskin sect. 16.5, leading to the gluon 1-loop correction to the gluon propagator (16.70). If you prefer to compute the beta function (16.85) by any other method, that is even better.

    Optional (but it would give you the full satisfaction): compute the beta function (16.85), read through sect 16.7 (without including any of it into the exam), derive the QCD running coupling constant (17.17), and finish off by reading through sect 17.6 (without including any of it into the exam).

            Due Tuesday June 6, 2000, at 12:00, Predrag's office.


    1. An Introduction to Quantum Field Theory, M.E. Peskin and D.V. Schoeder (Addison Wesley, Reading MA, 1995).
    2. Field theory, P. Cvitanovic'.
    3. Lattice Field Theory, P. Cvitanovic'.
    4. Group theory, P. Cvitanovic'.
    5. Quantum Field Theory, L.S. Brown (Cambridge University Press, Cambridge 1992).
    6. Field Quantization, W. Greiner and J. Reinhardt (Springer-Verlag, Berlin 1996).