Theory of Elementary Particles

Objectives

The main theme of the course is non-Abelian gauge theory in 3+1 dimensions.
Yang-Mills action, BRST quantization, renormalization, renormalization group (beta-function),
anomalies, theta angle, instantons, solitons, will be discussed.

Special Announcement:
The next lecture (Lecture 4) will be on May 7, Tuesday.

Hours and Rooms: Mondays 13:00-14:45 at Room 285 of Rigakubu-1-Go-Kan

Instructor:

Kentaro Hori
Kavli IPMU, Kashiwa Campus
kentaro.hori _at_ ipmu.jp

Course Plan:

Non-Abelian gauge theory: the classical theory

Quantization

Renormalization and Beta function

Anomalies

Theta Vacua

Yang-Mills instantons

Solitons

References:

Homepage of QFTII 2023-2024
Peskin and Schroeder, An Introduction to Quantum Field Theory
Weinberg, The Quantum Theory of Fields, I & II
Coleman, Quantum Field Theory: Lectures of Sidney Coleman (book), Notes from Sidney Coleman's Physics 253a (arXiv)
Kugo, Geijiba no Ryoushiron, I & II (J = in Japanese)

Grading Scheme: Reports.

Progress:

Lecture 1 (April 8): Conventions; Yang-Mills theory, Coupling to matter field: scalars, fermions.
Lecture 2 (April 15): Symmetry and Ward identity; Quantization of gauge theories.
Lecture 3 (April 22): Introduction to perturabation theory: Feynman diagrams, connected vs disconnected.

Additional notes:

For Lecture 1: Some math exercises
For Lecture 2: Path integrals ((a) examples, (b) symmetry-twisted partition functions, (c) Ward identities in a general dimensions)
                        Fermionic path-integrals ((a) amplitudes and partition functions, (b) multiple pairs of fermions, (c) ghost systems)
                        Right and left actions; Hermiticity of gauge fixed system
                        Quantization of gauge theories in operator formalism (symplectic view)
For Lecture 3: (a) Free theories, (b) Perturbative expansion is an asymptotic expansion, (c) Decomposition to connected parts.

Plan:

April 8: Conventions; Yang-Mills theory, Coupling to matter field: scalars, fermions; Quantization of gauge theories.
April 15: Symmetry and Ward identity; Quantization of gauge theories.
April 22: Introduction to perturabation theory.
May 7 (Tuesday!): 1PI effectiove action, Zinn-Justin equation.