Spring 2007

Solution to HW #7 posted

Misc Notes on Clifford Algebra (gamma matrices), tensor product and direct sum, steepest descent, Lorentz (Poincaré) symmetry, and FP ghosts (incomplete) and anomalies (incomplete)

Class Schedules

Lectures:	Tue Thu 9:30-11:00, 402 LeConte
Discussion sections:	Fri 2:00-3:00, 402 LeConte
Homeworks:	bi-weekly, due Tuesdays by the class
Exams:	take-home

Instructor: Hitoshi Murayama

E-mail:	hitoshi at berkeley.edu
Phone:	2-1019 (no voice machine), 486-6659 (LBNL, with voice machine)
Office:	411 Old LeConte Hall, 50A-5104D (LBNL)
Office Hours:	Tue 11-12

GSI: Frank Tackmann

E-mail:	ftackmann at berkeley.edu
Phone:	???, 486-4351 (LBNL, with voice machine)
Office:	??? Old LeConte Hall, 50-5047 (LBNL)

229A or equivalent

• Path Integral, Green's Functions and 1PI Effective Action
• General Theory of Renormalization
• Non-abelian Gauge Theory and Quantization
• Spontaneously Broken Gauge Theory
• Anomalies
• Topology of Gauge Theory
• Instantons and Non-perturbative Methods
• Supersymmetry (time permitting)
• Exact Results in Supersymmetric Gauge Theories (time permitting)

• Textbook: Michael E. Peskin and Daniel V. Schroeder, An Introduction to Quantum Field Theory, Perseus Books Group. Errata can be found here.
• Path Integral lecture notes written for 221A.
• Quantum Field Theory, I, II, III, Spontaneous Symmetry Breaking, lecture notes written for 221B. They in particular shows how quantum field theory is equivalent to quantum mechanics of identical particles when the number of particles is conserved, how partition functions can be computed, and how to apply them to work out excitation spectrum when symmetry is spontaneously broken.
• Model of spin originally written just for fun for 221A. It shows how spins can be put on path integral.
• Experimental test of the running mass of the bottom quark. P. Bambade, M.J. Costa, J. Fuster, P. Tortosa, Nucl. Phys. Proc. Suppl. 133 9-12 (2004)
• David J. Gross and André Neveu, "Dynamical symmetry breaking in asymptotically free field theories," Phys. Rev. D10 3235-3253 (1974).
• Alexander M. Polyakov, "Interaction Of Goldstone Particles In Two-Dimensions. Applications To Ferromagnets And Massive Yang-Mills Fields," Phys. Lett. B59 79-81 (1975).
• Sidney R. Coleman, R. Jackiw, and H. David Politzer, "Spontaneous symmetry breaking in the O(N) model for large N," Phys. Rev. D10, 2491 (1974)
• J. C. Le Guillou and J. Zinn-Justin, "Critical exponents from field theory," Phys. Rev. B 21, 3976-3998 (1980)
• Perturbative series as asymptotic expansion and its limitation, written for 221A.
• Sidney Coleman and Erick Weinberg, "Radiative Corrections as the Origin of Spontaneous Symmetry Breaking," Phys. Rev. D 7, 1888 - 1910 (1973)
• Howard Georgi, Lie Algebras in Particle Physics, Frontiers in Physics series, Perseus Books Group, is an excellent practical guide to group theory.
• L. Alvarez-Gaumé and P. Ginsparg, "The topological Meaning of non-Abelian Anomalies," Nucl. Phys. B 243, 449 (1984)

• Problem 9.2, due 1/26 for discussion section, and the solution
• Problem 10.2, due by class on 2/13, and the solution
• Problem 11.3, due by class on 2/27, and the solution
• Problems 11.1 and 12.2, due by class on 3/12, and the solution
• Part 2, "Final Project", as far as you can go, due by 3/23 (Fri) 4pm. If you need to work on it over the break, you can turn it in in class on 4/3. solution up to part (e).
• Problems 15.3 and 15.5, due by class on Apr 17, and the solution
• Problems 16.1 and 16.2, due by class on May 1 , and the solution

Notes on anomalies (incomplete)

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