Spring 2017

Prelude: current state of fundamental interactions

Lecture 1. Generalities about RG flows, (ir)relevant operators, EFTs, beta-functions and all that. UV cutoff. Example: beta-function in phi^4 in 4d.

HW1: beta-function in the theory of two scalar fields in 4d (3 couplings)

Lecture 2:

• Elastic unitarity as a way to fix UV cutoff.
• Vacuum instabilities: Ghosts and tachyons
• False vacuum decay a la Coleman. Example: negative quartic

HW2: Vacuum decay in scalar 4d theory with cubic self-interaction

Lecture 3 Nonlinear Sigma Model. Cosets. Equivalence Theorem. Relation to spontaneous global symmetry breaking. Examples: SO(N)/SO(N-1), SU(3)/SU(2)xU(1).

HW3 SO(5)/SO(3)xSO(2) sigma model

Lecture 4 Symmetry breaking perturbations in EFTs. Spurionic argument. Electromagnetic couplings. EM mass difference. EM effects in NLSM. Pion decay.

HW4

• Spurions in Yukawa theory with N fermions and one scalar
• EM mass difference for pions and for proton/neutron

Lecture 5

• Potential terms in NLSM. Vacuum alignment. Pseudogoldstones
• Chiral lagrangian for low energy QCD with 3 light quarks. Quantitative discussion of masses for the octet of mesons.

Lecture 5A

This was a bonus lecture about baryon masses and magnetic moments description using SU(3). The lecture was not given, but detailed lecture notes on the subject are available.

HW5

Filling in details in the meson mass discussion

Lecture 6

• Gauge invariance
• Unitarity and Reflection positivity

HW6

• Reflection positivity of Ising on the lattice
• Reflection positivity (or its absence) in the theory of elasticity and in Maxwell from 2pt function and via path integral

Lecture 7

• Gauge invariance, Part II
• Effective theories for gauge invariant theories: Euler-Heisenberg, neutral atoms

HW7 Loops in effective theories (using scalar with shift symmetry as example)