# Home: Wilsonian Renormalization and Effective Field Theories

## Pre-requisites

Students should have done a first course in quantum field theory including basic path integral methods, going from a Lagrangian to its Feynman rules, computing amplitudes and Born cross sections, and the basics of renormalization. This goes beyond the quantum field theory course given in the SERC preparatory schools in THEP. A knowledge of the Standard Model at the level of the corresponding course given in SERC preparatory schools in THEP will be assumed.

## Reference material

- Quantum Theory of Fields, Vol II (Modern Applications), by Steven Weinberg.
- Effective Field Theory, by Howard Georgi, in Annual Reviews of Nuclear and Particle Science 43 (1993) 209.
- Effective Field Theories, by David B. Kaplan [arXiv:nucl-th/9506035]
- Effective Field Theories, by Aneesh V. Manohar [arXiv:nucl-th/9606222]

## Lecture notes

- Lecture 1: Effective Theories are Dimensional Analysis
Natural units; universality; irrelevant, relevant and marginal couplings; fine-tuning problem; Fermi theory of $\beta$-decay; low-energy effective theory; operator product expansion; super-renormalizable, renormalizable and non-renormalizable theories; naturalness; cosmological constant; strong CP problem; Higgs mass; chiral symmetry; landscape; Hoyle coincidence; anthropic principle.

[Lecture 1]- Lecture 2: Regularization and renormalization
Loop integrals; ultraviolet cutoff scale; cutoff regularization; large logarithms; dimensional regularization; mass-independent regularization; counter-terms; renormalization scheme; renormalization scale; $msbar$ renormalization scheme; un-renormalizable theory; renormalizable Lagrangians; super-renormalizable couplings; Chiral Ward identities.

[Lecture 2]- Lecture 3: Wilsonian renormalization
Wave-function renormalization; Callan-Symanzik beta-function; fixed point; running coupling; coarse-graining; central limit theorem; Landau pole; lattice field theory; Ising model.

[Lecture 3]- Lecture 4: More dimensional analysis and scale anomalies
Regularization; scale invariance; scaling hypothesis; fractals; anomalous dimension; fractal dimension; scale anomaly; renormalized variables; renormalization group; homogenous functions; Compton scattering; Bhabha scattering; renormalization group equations.

[Lecture 4]- Lecture 5: The EFT of Dark Matter Detection
Classical general relativity; natural length scale; Schwartzschild radius; critical density; Hubble scale; scale of galactic clusters; flat rotation curves; Velocity distributions of galaxies in clusters; CMB anisotropies; local density and velocity of dark matter; relic density; primordial density; chemical equilibrium; WIMP miracle; Galilean invariance; power counting rules; spin-independent elastic cross sections; spin-dependent elastic cross sections.

[Lecture 5]- Lecture 6: Effective Field Theory Methods in Atomic and Nuclear Physics
Shell model, Landau-Fermi liquid; superconductivity; Wigner's semi-empirical mass formula. [Lecture 6]

- Lectures 7 and 8: Symmetries in Effective Field Theory
Accidental low-energy symmetries; hard breaking of symmetry; softly broken symmetry; flavour-changing neutral currents; Isgur-Wise symmetry; custodial symmetry; conformal symmetry; Goldstone boson; vacuum expectation value; generating functional; effective action; effective potential; Goldstone modes; no tadpole corrections; pseudo-Goldstone bosons; chiral symmetry; explicit breaking of symmetry; helicity projection; anomaly; baryon number; spurion; pion decay constant; chiral perturbation theory; quark condensate. [Lectures 7 and 8 (single file)]

- Lecture 9: QFT at Finite Temperature
Plasma; mobile charges; plasma parameter; Debye screening; space charge; plasma oscillations; Langmuir waves; plasmons; plasma frequency; Landau damping; dimensional reduction; free energy; pressure; Braaten-Pisarski resummation; magneto hydro-dynamics; non-Abelian magnetic screening. [Lecture 9]

Copyright: Sourendu Gupta; Last modified on 17 Jan, 2019.