Physics 615, Fall 2007

Overview of Quantum Field Theory

Lecture and Supplementary Notes

Joel Shapiro

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Lecture Notes

Note: This is a tentative schedule, subject to change as we go along.

Latexed Lectures are available in full format for easier on screen reading, and reduced to two pages/side for more efficient printing. Click on "view" or "print" respectively. Here are errata that have been fixed, to view or to print.

Item	Date	Topics	Reference	Pages
L1	Sept. 6	Introduction, classical mechanics	Introduction: (view, print)	pp 1-8(?)
L2	Sept. 10	Fields, QM	Intro, continued	pp 8-18 (?)
L3	Sept. 13	Momentum; Propagator	Intro, continued	pp 18-26
L4	Sept. 17	Noether's Theorem	Lect 4 (view/print) noether (view, print)	p. 1 pp. 1-8
L5	Sept. 20	First Appl. of Noether	First Apps: (view, print)	pp 1-8
L6	Sept. 24	The Poincare Group	Lorentz Trans.(view, print)	pp 1-10
L7	Sept. 27	General Rep of Poincare Dirac and Weyl Fields	Lorentz Trans. Lect 7(view, print)	pp 8-10 pp 1-6
L8	Oct. 1	Dirac Solutions	Lect 8 (view, print) Peskin and Schroeder	pp 1-2 pp 45-51
L9	Oct 4	Quantization of ψ	Lect 9 (view, print) Peskin and Schroeder	pp 1-2 pp 58-59, 61-65
L10	Oct. 8	P, C, and T	Lect 10 (view, print) Peskin and Schroeder	pp 1-2 pp 65-71
L11	Oct. 11	Interacting Fields	Intro (view, print) Peskin and Schroeder	pp 1-2 pp 77-87
L12	Oct. 15	Wick's Theorem, Feynman Diagrams	Lect 12: (view), print) Peskin and Schroeder	pp. 1-2 pp 88-99
L13	Oct. 18	Cross sections, S-matrix	Peskin and Schroeder	pp 99-108
L14	Oct. 22	S matrix from Feynman diagrams	Lect 14: (view), print) Peskin and Schroeder	pp. 1-2 pp 108-120
L15	Oct. 25	Yukawa, QED rules	Lect 15: (view/print) Peskin and Schroeder	p. 1 118-126
L16	Oct. 29	e+e-  → μ+μ- cross section, crossing symmetry	Lect 16: (view/print) Peskin and Schroeder	p. 1 131-141, 153-158
Note: we will skip sections 5.2 and 5.3
L17	Nov. 1	crossing symmetry; Compton Scattering	Peskin and Schroeder Algebra for P. 161 view,print	153-169 1-4
L18	Nov. 5	Radiative corrections; Bremsstrahlung	Peskin and Schroeder Note on p179 view,print	175-182 1-3
L19	Nov. 8	Quantum Bremsstrahlung, vertex corrections	Lect 19: (view, print) Peskin and Schroeder Schwinger (view, print)	1-2 182-189 1-3
L20	Nov. 12	Anomolous Magnetic Moment	Lect 20: (view, print) Peskin and Schroeder	1-4 190-196, 211-214
Note: we will skip sections 6.4, 6.5, 7.2, 7.3 and 7.4.
L21	Nov. 15	Renormalization, electron self-energy Σ2 Charge Renormalization	Lect 21: (view, print) Peskin and Schroeder	1-4 215-222
L22	Nov. 19	Z2, Π2, Dimensional Regularization	Lect 22: (view, print) Peskin and Schroeder Notes on area of Sd-1, Γ(z) and B(x,y) below	1-3 244-252
L23	Nov. 20	Finite effects of Π2, Renormalization Spont. Sym. Breaking, Goldstone	Lect 23: (view, print) Peskin and Schroeder	1-4 252-256 347-352
	Nov. 22	NO CLASS, enjoy Thanksgiving
L24	Nov. 26	Gauge Invariance	Lect 24 (view/print) Gauge Theory, Part 1 (view, print)	p. 1 pp 1-8
L25	Nov. 29	Gauge Field Lagrangian and equations	Lecture 25: view/print, Gauge Theory, Part 1 (view, print) Gauge Theory, Part 2 (view, print) Peskin and Schroeder	page 1 pp 9-15 pp 1-3 pp 506-507
L26	Dec. 3	Ward Identity, Fadeev-Popov	Lecture 26 (view, print) Peskin and Schroeder Gauge Theory, Part 2 (view, print)	pp. 1-3 pp 508-511 pp 3-5
L27	Dec. 6	Higgs Mechanism	Peskin and Schroeder	pp 689-696 pp 700-701
L28	Dec. 10 Last Class	Glashow Salam Weinberg Electroweak Theory	Lecture 28 (view, print) Peskin and Schroeder	pp 1-4 pp 701-705 pp 713-716

I expect to cover (!), or maybe cover (?) the following sections of Peskin and Schroeder:
6.1-3!, 7.1!, 7.5, 11.1, 15.1-2, 16.1, 20.1-2
Not covered: sections 6.4-5, 7.2-4, 8, 9, 10, 11.2-5, 12, 13, 14, 15.3-4, 16.2-6, 17-19, 20.3, 21, 22

Supplementary Notes

• Notation comparison: different books use different conventions. Here are some comparisons.
• Notes on totally antisymmetric tensors, or Levi-Civita symbols, ε_μνρ..., in 3-D Euclidean space: (view), (print), and in higher dimensional Euclidean or Minkowski space: (view), (print), including their use with matrices and determinants. The Levi-Civita symbol is also essential in curved spaces, but that is for another course.
  Also, on ε and determinants, "Properties of Determinants": (view), (print)
• On Indices and Arguments: (view), (print). Some cautionary notes on how indices are used and how to avoid making nonsense when evaluating expressions with dummy indices.
• On when plugging an "equation of motion" back into the Lagrangian is okay: (view), (print).
• Note on the Surface "Area" of a D-dimensional ball, and on the Euler Γ function ( (view), (print))
  and on the Beta function and Γ(ε) for ε ˜ 0 ((view), (print))
• Note on T^μν for electromagnetism: ((view), (print))

More advanced supplementary notes

Topic	One Column	Two Columns
Path Integral Formulation of Quantum Mechanics	view	print
Functional Integral for a Scalar Field	view	print
Gauge Theory on a Lattice	view	print
A short note on Fadeev-Popov Ghosts	view or print
some comments on BRST cohomology	view or print
Generating Functions	view	print

You asked for an introductory reference on supersymmetry. Here is a rather long one by Jim Gates.

Supplementary Notes

• Groups: You really ought to take a course on group theory, but if you haven't, here are
  • A lightning review (view, print) of their definition and representations, the connection of continuous groups to Lie algebras, Killing forms and Casimir operators.
  • A Note on Adjoint representation, Killing form and the antisymmetry of c_ij^k. (view, print)
  .
  • A Group Invariant Metric, which discusses a metric g_μν on the group with the property that lengths are preserved under multiplication by a common group element. As a consequence g^1/2 is the Haar measure. This is only for those interested, and is not of any direct relevance to this course.
• Comment on Integrals over Grassman Variables (view, print)