Rutgers University Department of
Physics and Astronomy
PHYSICS 619, SPRING 2018
Prof. David Shih
Office: Serin E370
Phone: (848) 445-9072
Office hours: By appointment
Lectures: Monday and Thursday, 10:20-11:40am,
This is a continuation of Physics 618, Fields I from Spring 2017. The
course format will be similar to that of Physics 618.
Previously you primarily used Srednicki's textbook.
All of Part I (spin 0) was covered.
There were also a couple of lectures on critical phenomena,
the Ising model and phi^4 theory which is not in Srednicki's book.
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, I will assume that you are familiar with the following concepts:
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)
quantization of scalar fields
(both Minkowski and Euclidean forms)
(PS: Chs. 9.1-9.3, 9.5)
(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 will be assigned at intervals of 1.5 or 2 weeks; they
will be graded and returned to you.
There will be no exams.
Students with disabilities:
Please read here.
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)
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
QUANTIZATION OF EM FIELD
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)
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 vertex function.
Magnetic moment of the electron.
(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
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
Geometry of gauge invariance.
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)
Renormalization in the Y-M theory.
One-loop divergencies. $\beta$-function.
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
(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)
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