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

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


Schwinger/Feynman Formulation of Field Theory

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


Renormalization


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


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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%).

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Non-Abelian Gauge Invariance
Suggested reading:

Peskin: Chap 15 - Non-Abelian Gauge Invariance


Quantization of Non-Abelian Gauge Theories
Suggested reading:

Peskin: Sects 16.1-16.4 - Quantization of Non-Abelian Gauge Theories,



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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.


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References

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).