next lecture | course info | description | FAQs | Field Theory notes | webbook help | Cvitanović schedule ]

Mar 31 2005

QUANTUM FIELD THEORY

next lecture

    -

  1. Feynman's Formulation of Quantum Field Theory
  2. QM Amplitudes as a Sum over Paths

    Lecture 1           12:05-13:25 Tue Jan 11
    Lecture 2           12:05-13:25 Thu Jan 13
    Lecture 3           12:05-13:25 Tue Jan 18
    Lecture 4           12:05-13:25 Thu Jan 20

    Reading:

    Cvitanović lecture notes,
    Quantum Field Theory, version 3.0, or - reordered and partially proofread:
    Quantum Field Theory - a cyclist tour, version 3.3
    (preliminary: Please print the bare minimum - needs lots of editing).

    Other references covering some of the same ground:

    M. Srednicki, Quantum Field Theory, Part I: Spin Zero - hep-th/0409035: Chapters 6-8


    Peskin: Chap 9 - Functional Methods
    Brown: Chap 1 - Functional integrals (Very clear)
    Greiner & Reinhardt, example 11.2: Weyl ordering for operators
    Greiner & Reinhardt, exercise 11.1: Path integral for a free particle

    problem set 1 - due Tue Jan 25:

    problem 28.1 - Gaussian integral, derivation

    problem 28.2 - Dirac delta function

    problem 28.* - Derive the Fresnel integral

    problem 28.3 - D-dimensional Gaussian integrals

    problem 28.4 - Stationary phase approximation in higher dimensions.

    bonus problem (easy) - derive Sterling's formula by saddle-point method

    bonus problem (medium hard) - Quantize harmonic oscillator by path integral
    Solution: Lippolis et al. notes, Feb 4 2005

    A nice discussion - Gaussians galore:

    L.P. Kadanoff, Statistical Physics; Statics, Dynamics and Renormalization, Chapter 3: Gaussian Distributions
    Physics Today review

    Lecture 5           12:05-13:25 Tue Jan 25
    Lecture 6           12:05-13:25 Thu Jan 27
    Lecture 7           12:05-13:25 Tue Feb 1
    Lecture 8           12:05-13:25 Thu Feb 3

    problem set 2 (and more on exer5.A.1) - due Thu Feb 10

    Lecture 9           12:05-13:25 Tue Feb 8
    Lecture 10           12:05-13:25 Thu Feb 10

    problem set 3 - due Thu Feb 17

    A nice discussion of free propagation as Brownian walks:

    C. Itzykson and J.-M. Drouffe, Statistical field theory, vol 1 and 2 (Cambridge U. Press, 1991)
    Chapter 1: From Brownian motion to Euclidean fields

    -

  3. Schwinger/Feynman Formulation of Field Theory
  4. Reading:

    Chapters 1-3 of Field Theory. 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.

    Other references covering some of the same ground:

    M. Srednicki, Quantum Field Theory, Part I: Spin Zero - hep-th/0409035: Chapters 8-10
    Peskin: Chap 4 - Interacting Fields and Feynman Diagrams

    Lecture 11           12:05-13:25 Tue Feb 15
    Lecture 12           12:05-13:25 Thu Feb 17

    problem set 4 - due Thu Feb 24
    solution 2.I.3

    To balance A. Hanany's pied piper song - a delightful sceptics view:

    Freeman J. Dyson, The World on a String

    A historical article on Feynman diagrams:

    D. Kaiser, American Scientist 93, 156 (2005) Physics and Feynman's Diagrams:
    For very brief history, see page 41 of: P. Cvitanović,

    character building: If you want to work through my presentation of group theoretical projection operators, the method is in the appendix A of

    Quantum Field Theory - a cyclist tour (text identical to the version posted in January),
    in Sect 3.6 of P. Cvitanović, Group Theory,
    and in Harter's appendix on group theory in W.G. Harter and N. Dos Santos 1978 article.

    curiosity:

    Hamilton's turns: how Hamilton (who would have guessed...) used quaternions to to extend the discrete Fourier transform from a circle to a sphere.

    Lecture 13           12:05-13:25 Tue Feb 22
    Lecture 14           12:05-13:25 Thu Feb 24

    problem set 5 - due Thu Mar 3
    reading: Chapter 3. Path Integrals

    A. Zee on attractive/repulsive particle exchanges Typos, chapter 3

    Lecture 15           12:05-13:25 Tue Mar 1
    Lecture 16           12:05-13:25 Thu Mar 3

    problem set 6 - due Thu Mar 10
    solution 8.1, 8.2, problem 3
    reading: Srednicki Chap. 8

    Lecture 17           12:05-13:25 Tue Mar 8
    Lecture 18           12:05-13:25 Thu Mar 10

    problem set 7 - due Thu Mar 17
    reading: Chapter 4. Fermions
    what you need to know about fermions

    Lecture 19           12:05-13:25 Tue Mar 15
    Lecture 20           12:05-13:25 Thu Mar 17

    -

    Midterm recess: spring break week, Mar 21 to Mar 25 2004

    -

    problem set 8 - due Thu Mar 31
    reading:

    W. Greiner and J. Reinhardt: Dirac equation.

    Lecture 21           12:05-13:25 Tue Mar 29
    Lecture 22           12:05-13:25 Thu Mar 31

    problem set 9 - due Thu Apr 7
    reading: Chapter 5, sections B, C; Chapter 6, sections A, B

    Rest of the schedule is preliminary

    Lecture 23           12:05-13:25 Tue Apr 5
    Lecture 24           12:05-13:25 Thu Apr 7

    Lecture 25           12:05-13:25 Tue Apr 12
    Lecture 26           12:05-13:25 Thu Apr 14

    Lecture 27           12:05-13:25 Tue Apr 19
    Lecture 28           12:05-13:25 Thu Apr 21

    Lecture 29           12:05-13:25 Tue Apr 26
    Lecture 30           12:05-13:25 Thu Apr 28

    Dirac spinor exercises, due Thu, ?? 2005

    -

  5. Renormalization

  6. Reading due Tue, Apr 1 2005
    Exercises due Thu, Apr 3 2005
    Reading due Tue, Apr 8 2005
    Exercises due Tue, Apr 15 2005

    Friday Apr 29:    classes end


    Final exam: takehome - posted here Friday, Apr 29, 2005, at 4PM.

    Goals:
    We work through the 1-loop renormalization for the phi^3 scalar field theory, in order to verify to the lowest order the general renormalization theory developed in the last part of the course. We also learn how to use dimensional regularization in order to evaluate explicitely the divergent integrals.

    Required:
    problem (1) Dimensional analysis
    problems (2) (3) (6) (7) (8)

    Browny points:
    problems (4) (5) (9) (10)

            Due no later than Monday, May 2, 2005 at 10:00, Predrag's office.

    Solution:

    Have a good summer!


    References

    1. M. Srednicki, Quantum Field Theory, Part I: Spin Zero - hep-th/0409035
    2. P. Cvitanović, Path integrals, and all that jazz, (preliminary unedited notes are here: Please send me your edits!)
    3. P. Cvitanović, Field theory
    4. A. Zee, Quantum Field Theory
    5. M.E. Peskin and D.V. Schoeder, An Introduction to Quantum Field Theory, (Addison Wesley, Reading MA, 1995).
    6. M. Srednicki, Quantum Field Theory, Part II: Spin One Half - hep-th/0409036
    7. Group theory, P. Cvitanović.
    8. Quantum Field Theory, L.S. Brown (Cambridge University Press, Cambridge 1992).
    9. Field Quantization, W. Greiner and J. Reinhardt (Springer-Verlag, Berlin 1996).

    -