# Home: Effective Field Theories

## Pre-requisites

Knowledge of the classical Lagrangian of Abelian and non-abelian gauge theory; knowledge of basic quantum field theory; ability to obtain Feynman rules and compute amplitudes, rates and cross sections at tree level; familiarity with the need of performing renormalization; exposure to renormalization of either scalar field theory or quantum electrodynamics.

## 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 and 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; Hoyle coincidence; anthropic principle.

[Lecture 1]- Lecture 2: Wilsonian 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.

Wave-function renormalization; Callan-Symanzik beta-function; fixed point; running coupling; coarse-graining; central limit theorem; Landau pole; lattice field theory; Ising model.

[Lecture 2]- Lecture 3: Scale anomalies and dimensional analysis
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 3]- Lecture 4: 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. [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]

Copyright: Sourendu Gupta; Last modified on 14 Dec, 2017.