Rutgers University Department of Physics and Astronomy

# FIELDS II

## GENERAL INFORMATION

Instructor:

Prof. Duiliu-Emanuel Diaconescu
Office: Serin E358
Email: duiliu@physics.rutgers.edu
Phone: (848) 445-9054
Office hours: By appointment online.

Lectures: Tuesday and Thursday, 10:20-11:40am, online via Webex.

Textbooks:

Prerequisites:

Physics 618, Fields I.

If you did not take Fields I, it is your responsibility to do background reading to make sure you understand the concepts in this course. Specifically, familiarity with the following concepts will be assumed:

• Canonical quantization of scalar fields (M. Peskin, D. Schroeder: Chs. 2,3)
• Renormalized perturbation theory (phi^3 and phi^4 theories) (PS: Chs. 4.1-4.4, 4.7, 10.1-10.2)
• Path-integral quantization of scalar fields (both Minkowski and Euclidean forms) (PS: Chs. 9.1-9.3, 9.5)
• Renormalization Group (PS: Chs. 12.1-12.3)
• General form of the spectrum in QFT, S-matrix, LSZ formalism (PS: Chs. 4.5, 4.6, 7.1-7.3)
• Spontaneous Symmetry Breaking (PS: Ch. 11.1)

Homeworks: Homeworks will be assigned at intervals of 1.5 or 2 weeks; they will be graded and returned to you.

Exams: There will be no exams.

## DETAILED SYLLABUS

This is a tentative schedule of what we will cover in the course. It is subject to change, often without notice. These will occur in response to the speed with which we cover material, individual class interests, and possible changes in the topics covered. Use this plan to read ahead from the text books, so you are better equipped to ask questions in class.

QUANTIZATION OF SPIN 1/2 FIELD

• Classification of fields with spin: representations of the Lorentz group (Srednicki 34-35)
• Lagrangians for spin 1/2 fields: Weyl, Majorana, Dirac. Free particle wavefunctions. (Srednicki 36)
• Canonical quantization, LSZ reduction (Srednicki 37-39, 41)
• Discrete symmetries (Srednicki 40)
• Free propagator, fermionic path integrals, Feynman rules, Yukawa theory (Srednicki 42-45)

• QUANTIZATION OF EM FIELD

• Canonical quantization: General aspects of quantization of systems with constraints. Maxwell's equations. EM field as a dynamical system with constraints. Quantization in the Coulomb gauge. (Srednicki 33, 54-56)
• Covariant path integral quantization: Euclidean path integral. Gauge group. Gauge fixing conditions. Faddeev-Popov trick. Feynman propagator. (Peskin 9.4)
• QUANTUM ELECTRODYNAMICS

• Lagrangian and Feynman rules: Feynman rules for QED. Gauge invariance of the scattering amplitudes. Electron vertex function (formal structure). (Srednicki 58-59; Peskin 4.7, 5.1, 6.2)
• One-loop radiative corrections: Electron propagator. Electron vertex function. Ward-Takahashi identity. Magnetic moment of the electron. Infrared divergence. (Srednicki 62-64, 67; Peskin 6.3-6.5, 7.1, 10.3)
• Renormalized Perturbation Theory: Vacuum polarization: formal structure. Renormalized action and counterterms. Pauli-Villars and dimensional regularizations. Vacuum polarization: evaluation. (Peskin 10.1, 10.3; Srednicki 62)
• Renormalization group in QED: Radiative corrections to the Coulomb law. Callan-Symanzik equation. Beta-function. (Peskin 10.3, 12.3; Srednicki 66)
• NON-ABELIAN GAUGE THEORIES

• Gauge invariance: Geometry of gauge invariance. Wilson loop. Yang-Mills Lagrangian. Basic facts about Lie algebras. Yang-Mills for an arbitrary compact group. (Peskin 15.1-15.4; Srednicki 69, 70)
• Quantization of non-Abelian gauge theories: Path integral quantization. Feynman rules. Ghosts and unitarity. BRST symmetry. (Peskin 16.1-16.3; Srednicki 71, 72, 74)
• Asymptotic freedom: Renormalization in the Y-M theory. One-loop divergencies. $\beta$-function. Quantum Chromodyanamics. Background field method. Functional determinants. Seley coefficients. (Peskin 16.5-16.7, 17.1-17.2; Srednicki 73, 78)
• AXIAL CURRENTS IN GAUGE THEORIES (ANOMALIES)

• Axial current in four dimensions (Peskin 19.2; Srednicki 73, 76, 77)
• Goldstone bosons and chiral symmetries in QCD (Peskin 19.3; Srednicki 83)
• GAUGE THEORIES WITH SPONTANEOUS SYMMETRY BREAKING

• Higgs mechanism (Peskin 20.1; Srednicki 84)
• Quantization of spontaneously broken gauge theories (Peskin 20.1; Srednicki 85, 86)
• Glashow-Weinberg-Salam theory of weak interactions (Peskin 20.2; Srednicki 87-89)