Phys 518, Spring 2017

Topics Covered in Each Lecture

Lecture Number	Date	Content	Corresponding Reading material
1	Feb. 07	Infrared divergences: Two-particle elastic scattering of massless particles in phi^3-theory, scattering amplitude for splitting one of the outgoing particles, soft and colinear particles, the source of divergence for phi^3-theory in 6 dimensions	PPages 157-159 of Srednicki
2	Feb. 09	Calculation of the observed probability for an imperfect detector, the persistence of singularity in the zero-mass limit	PPages 159-161 of Srednicki
3	Feb. 14	Modified minimal subtraction as an alternative renormalization scheme, calculation of the self-energy, physical mass as a pole of exact propagator, the residue at this pole, 3-point vertex function	PPages 162-165 of Srednicki
4	Feb. 16	Corrections to LSZ in the modified minimal subtraction prescription; Calculation of the observed probability for an imperfect detector using the modified minimal subtraction, beta function and asymptotic freedom.	PPages 164-167 of Srednicki
5	Feb. 21	The bare and renormalized fields and parameters, the mu-independence of the bare quantities and its consequences: Direct calculation of the beta function and anomalous dimension of mass	PPages 169-173 of Srednicki
6	Feb. 23	The bare propagator and the Callen-Symanzik equations; Representations of the Lorentz group: Lorentz transformation of a scalar field operator as a unitary adjoint representation; the vector and rank-2 tensor representations; the reducibility of the rank-2 tensor representations into antisymmetric, traceless symmetric and full trace subrepresentations; the general structure of the irreducible unitary representations	PPages 173-174 & 205-208 of Srednicki
Homework 1
7	Feb. 28	Left- and right-handed spinor: Derivation of an expression for generators of Lorentz transformations in spinor representations	PPages 209-211 of Srednicki
8	Mar. 02	Expressing the  (2,1)x(2,1) representation so(1,3) as the direct sum of irreducible representation, the inverse of Levi Civida symbol eab in two-dimensions and its Lorentz-invariance. Lowering and raising the left spinor indices using epsilonab and the Levi Civita symbol epsilon^ab, the (2,2) representation of so(1,3), the vector fields, and the associated so(1,3)-invariant.	PPages 211-213 of Srednicki
9	Mar. 07	Decomposition of antisymmetric rank two tensor fields into a sum of self-dual and anti-self-dual fields; expression of S^{\mu\nu}_L and S^{\mu\nu}_R in terms of the invariants \Sigma_{a\dot a}^\mu	PPages 214-218 of Srednicki
10	Mar. 09	A not on spinor notation, \bar\sigma^mu, the Lorentz transformation property and adjoint of  \psi^\dagger\bar\sigma^\mu \chi	PPages 218-219 of Srednicki
Homework 2
11	Mar. 14	A Lagrangian density for spin 1/2 fields, supernumbers, functions of a supernumber, differentiation and integration of differentiable functions of anticommuting variable	PPages 221-212 of Srednicki & Pages 1-10 of DeWitt
12	Mar. 16	Classical Lagrangian density, action, and the classical equations of motion for a spin 1/2 fields, teh Majorana field, Dirac gamma matrices, Dirac equation, Lagrangian density for a pair of noninteracting spin 1/2 fields and its So(2) symmetry	PPages 222-225 of Srednicki
13	Mar. 21	Classical field equations for a pair of free noninteracting spin 1/2 fields, Dirac spinor field, expressing the Lagrangian density and its So(2) (U(1)) symmetry in terms of the Dirac fields, the conserved Nother current associted with this U(1) symmetry, extension of this symmetry to O(2) and the charge conjugation	PPages 225-228 of Srednicki
14	Mar. 23	Lorentz transformation property of the Majorana and Dirac fields, Canonical quantization of a free spin 1/2 particle, the conjugate momentum to a spinor field and the Hamiltonian density, the emergence of constraints, a remark on quantization in the level of the Lagrangian density and the Peierls bracket; the canonical anticommutation relations for spinor fields, Dirac fields, and Majorana fields, Feynman slash notation, and the relation between solutions of the Dirac and Klein-Gordon equations	PPages 228-235 of Srednicki
Homework 3
15	Mar. 28	General solution of the Dirac equation, the pseudo-Hermiticity properties of the Dirac matrices, and biorthogonality relations for the eigenvectors of Dirac operator (-\gamma^\mu p_\mu).	PPages 235-239 of Srednicki  & Reading material on pseudo-Hermitian operators
16	Mar. 30	The biorthonormal system for the Dirac operator and its completeness, derivation of various identities satisfied by the eigenvectors of the Dirac operator and its adjoint	PPages 239-240 of Srednicki  & Reading material on pseudo-Hermitian operators
17	Apr. 04	Other identities satisfied by the eigenvectors of the Dirac operator and the charge-conjugation matrix	PPages 240-243 of Srednicki
18	Apr. 06	Canonical quantization of the Dirac spinor, the Hamiltonian operator of a free Dirac field	PPages 244-248 of Srednicki
Spring Break
Homework 4
19	Apr. 18	The charge operator, and quantization of a free Majorana field; parity and time-reversal transformations of a Dirac field.	PPages 248-257 of Srednicki
20	Apr. 20	Parity, time-reversal, and charge-conjugation transformations of basic bilinear constructed using a Dirac field, the CPT theorem; Basic scattering setup for interacting spin 1/2 field theories, the scattering amplitude	PPages 257-263 of Srednicki
21	Apr. 21	Extra lecture:  Derivation of the LSZ formula and its consistency conditions for Dirac fields.	Pages 263-266 of   Srednicki
Homework 5
Midterm Exam
22	Apr. 25	Free propagator for free Dirac fields, vacuum expectation value of time-ordered product of up to four Dirac fields, Partition function and its evaluation using path integration techniques for free Dirac fields, extension to interacting Dirac fields and its application in evaluating vacuum expectation value of time-ordered product of Dirac fields	PPages 267-274 of Srednicki
-	Apr. 27	No class (Made-up on April 21)
23	May 02	Yukawa theory: Dimension of the coupling constant, position-space Feynman diagrams, Calculation of vacuum expectation value of time-ordered expansion for the e^- \phi -> e^- \phi and e^- e^- -> e^- e^-.	PPages 282-285 of Srednicki
24	May 04	Scattering amplitude for e^- \phi -> e^- \phi and the momentum-space Feynman diagrams for Yukawa theory, the momentum-space diagrams for e^- e^- -> e^- e^-.	PPages 285-290 of Srednicki
Homework 6
25	May 09	Tree-level average cross sections for e^- \phi -> e^- \phi and e^- e^+ -> e^- e^+ scattering processes. Gamma matrix technology: Calculation of the trace of the product of n gamma matrices.	Pages 292-295 of Srednicki
26	May 11	Traces of the product of an odd number of gamma matrices, arbitrary four-vectors, pseudo-vectors, and their products.	Pages 295-297 of Srednicki

Note: The pages from the textbook listed above may not include some of the subjects covered in the lectures.