Effective Field Theories

Roots in a waste land
Lecture days
February 29 to March 3

Effective Field Theories

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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

  1. Quantum Theory of Fields, Vol II (Modern Applications), by Steven Weinberg.
  2. Effective Field Theory, by Howard Georgi, in Annual Reviews of Nuclear and Particle Science 43 (1993) 209.
  3. Effective Field Theories, by David B. Kaplan [arXiv:nucl-th/9506035]
  4. 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, 2018.