An Introduction to Effective Field Theory

Abstract

This review summarizes Effective Field Theory techniques, which are the modern theoretical tools for exploiting the existence of hierarchies of scale in a physical problem. The general theoretical framework is described, and explicitly evaluated for a simple model. Powercounting results are illustrated for a few cases of practical interest, and several applications to Quantum Electrodynamics are described.

Inflation and String Theory

“…Instead a so-called matching calculation order by order in perturbation theory is usually more practical [177][178][179][180].…”

“…At first order in b , the power spectrum is [36] 180) where φ k φ − √ 2 ln(k/k ) is the field value at horizon exit of the mode k. We have defined n s = 1 + 2η − 6 and 181) in units where M pl ≡ 1, and have worked to leading order in f / √ 2 . For the special case p = 1, i.e.…”

Point-particle effective field theory III: relativistic fermions and the Dirac equation

“…In particular, for relativistic spinless particles an interesting regime was identified for which energy shifts of S-wave states due to the source's finite size scale as 1) where the last factor is the S-wave Schrödinger-Coulomb wave-function at the origin |ψ(0)| 2 ∝ (mZα/n) 3 . Effects like this, scaling linearly with R, are unusual and so lead to the question of whether similar shifts occur for the spin-half electrons and muons that arise in conventional and muonic atoms.…”

“…Effective field theories [1][2][3][4] are the natural language for exploiting this kind of simplicity, though these are usually only formulated in a second-quantized language with all species of particles represented by their respective quantum field. For instance two-body contact interactions between two species of particles in a fully second-quantized framework would be represented in terms of their respective fields by terms like g(ψ * ψ)(χ * χ) in an effective Lagrangian.…”

Scalar gravitational waves in the effective theory of gravity

“…2 Effective Field Theory (EFT) methods have been developed and successfully applied in a number of areas from nuclear and particle physics to condensed matter physics [8][9][10][11][12][13][14][15][16][17]. The key hypothesis in the EFT approach is the decoupling of short and long distance scales, making possible a description of physics at energies far below an ultraviolet (UV) cutoff scale M by a set of local operators consistent with low energy symmetries.…”