Effective Field Theory
A. Pich
TL;DR
Effective Field Theory provides a principled framework for describing low-energy physics by integrating out heavy degrees of freedom and encoding their effects in a tower of local operators. The approach relies on a momentum (derivative) expansion, organizing operators by dimension and retaining a finite set of couplings at any fixed order, while preserving the correct infrared behavior of the underlying theory. Through concrete examples like the Euler–Heisenberg Lagrangian, Rayleigh scattering, and the Fermi theory, the text illustrates how high-scale physics leaves calculable imprints via Wilson coefficients and how quantum loops are treated within mass-independent renormalization schemes. It also outlines operator classification into relevant, marginal, and irrelevant, and points to extensions such as Chiral Perturbation Theory, Heavy Quark EFT, and electroweak chiral EFT, underscoring the broad applicability of EFT in particle physics.
Abstract
These lectures provide an introduction to the basic ideas and methods of Effective Field Theory, and a description of a few interesting phenomenological applications in particle physics. The main conceptual foundations are discussed in sections 2 and 3, which cover the momentum expansion and the most important issues associated with the renormalization process. Section 4 presents an overview of Chiral Perturbation Theory, the low-energy realization of Quantum Chromodynamics in the light quark sector. The Chiral Perturbation Theory framework is applied to weak transitions in section 5, where the physics of non-leptonic kaon decays is analyzed. The so-called Heavy Quark Effective Theory is briefly discussed in section 6. The electroweak chiral Effective Field Theory is described in section 7, which contains a brief overview of the effective Lagrangian associated with the spontaneous electroweak symmetry breaking. Some summarizing comments are finally given in section 8.