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c.zachos.k@att.net F422 C K Zachos
Quantum Field Theory III [Physics 428-3] Northwestern University
F210 M,F 11-12:30 (+)
Text: Matthew Schwartz, QFT & the SM
"The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction." [Sidney Coleman]
LINKS
Wikipedia : Baker–Campbell–Hausdorff_formula Lie_algebra Derivative_of_the_exponential_map
Pauli_matrices Rotation_group_SO(3) # A_note_on_representations Gell-Mann_matrices Irreps for SU(3)
Yang–Mills_theory Functional determinant Faddeev-Popov ghosts Higgs mechanism Chiral Anomaly Grand unification
Peskin & Schroeder: Introduction-to-Quantum-Field-Theory
Sterman: An Introduction to Quantum Field Theory
Okun: Leptons & Quarks [a superb booklet to own and come back to, again & again & again]
P Ramond: Journeys beyond the standard model
Alvarez-Gaume & Vasquez-Mozo, Introductory QFT
B de Witt, J Smith & E Laenen: Field Theory in Particle Physics
David Tong: Lectures on Quantum Field Theory
Cahn: Semi-simple Lie algebras & their reps
R Slansky (1981): Group theory for....
Wu-Ki-Tung: Group-Theory-in-Physics
B Hall: An Elementary Introduction to Groups and Representations
Crib Notes on Campbell-Baker-Hausdorff expansions
Lectures
Lectures
Weeks 1 & 2 & 3: Remedial Lie Group theory; Global SU(2)-symmetric theories; Currents and charges;
Gauge invariance; Gauge theory; Gauge fixing; Ghosts.
Read S, Chapter 25; ↯Notes , and Also
Weeks 4 & 5: Spontaneous symmetry breaking. Goldstone analysis. Current algebra modeling.
Linear, non-linear, and chiral σ-models. Chiral symmetry breaking. Higgs mechanism.
Read S, Ch 28.1,2,3; ↯Notes
Weeks 6 & 7: The Standard Model (EW); point of SU(2)⊗U(1); Bosons, weak angle, parameters;
Fermions and quantum numbers; Fermion masses; generation mixing; FCNC; GIM; CP violation;
neutrino masses.
Read S, Ch 29.1-5 ↯Notes
Weeks 7 & 8: μ decay; W and Z decay. RG in QCD & asymptotic freedom.
Read S, Ch 26 (esp 26.5, 26.6) ↯Notes
Weeks 9 & 10: Chiral triangle Anomalies, good vs bad. π→ 2γ ; Species counting; Constraints; SM cancellation.
WZW flavor chiral effective action term. Path integral measure non-invariance.
Read S, Ch 30 (esp 30.1, 30.4) ↯Notes
If they can get you asking the wrong questions, they don't have to worry about answers. [Thomas Pynchon, "Gravity's Rainbow"]
Homework Do more than half the problems assigned
First set Due May 1
Problem 1: Find c, k̂ as simple functions of a, b, n̂ and m̂.
Problem 2: Is the doublet 2 real? What is its S? Is the 3 real? Can you find the S for each of the bases you saw?
Are all irreps of SU(2) real? [Hint: Consider real eigenvalues of hermitean operators paired up in opposite pairs!]
Ditto for SU(3)? [Find counterexample in fundamental].
Problem 3: Check the coproduct Δ(J) obeys the same Lie algebra as the J.
What is its Casimir C₂? Can it be written in terms of the Casimirs of the m and n?
Problem 6: Show fabc , in our normalization conventions here, is totally antisymmetric in all three, not just two, indices. Is dabc likewise
totally symmetric? For SU(2), what is TR for general j ? Why?
Problem 7: S book prob 25.2 & 25.4.
Second set Due May 22
Problems 9: Check that pieces with no derivatives in the topological, θ, term of QCD vanish by symmetry. Can you express the rest as a surface term?
Can you have two derivatives acting on everything? Do prob 25.1.
Extract the couplings to Aμ s and two Aμ s of the matter fields and compare to the global Noether isospin currents thereof.
What is the total Noether current of the entire theory?
Problem10: Check that, on-shell (=by use of the E-L equations of motion),
Dabμ ( jμb(F) + jμb(B) ) =0
adjoint covariant [Hint for slick version: Jacobi on eqns of motion].
Hence, ipso facto!, ∂μ( jμa(F)+ jμa(B) ) ≠ 0 ,
by moving the 2nd term of the left-hand-side to the right hand side.
Problem 11: S problem 25.5.
Problem 12 [extra credit]: Include Pauli-moment term in the action, and augment Probs 10, 11, with its effects.
Problem 15: S problems 28.1 and 28.2
Problem 16: Using the expression for U linear in τ , work out some subleading terms (...) in each of the four currents
of the chiral model to appreciate their structure.
Third set, Due June 1
Problem 20: S problem 29.6
Problems 21: S problem 29.7 -- must do
Could do some cross sections in that chapter's S probs for your private edification.... but don't turn them in.
Catch blackboard bloopers.......
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