Introduction to Effective Field Theory

Draft version of an article prepared for the Encyclopedia of Mathematical Physics, Elsevier, to appear in 2006.

These notes are a written version of a set of lectures given at TASI-02 on the topic of effective field theories. They are meant as an introduction to some of the latest techniques and applications in the field.

We discuss a general model for effective quantum field theories (QFTs), which for example comprises quantum chromodynamics and quantum electrodynamics. We assume in the model a perturbative expansion of the Lagrangian with respect to a cut-off-energy parameter. For each order in the expansion we rigorously derive a representation, which is unitarily equivalent to the representation of the effective QFT in the non-interaction approximation. We interpret the various representat...

These lectures aim to provide a pedagogical introduction to the philosophical underpinnings and technical features of Effective Field Theory (EFT). Improving control of $S$-matrix elements in the presence of a large hierarchy of physical scales $m \ll M$ is emphasized. Utilizing $\lambda \sim m/M$ as a power counting expansion parameter, we show how matching an ultraviolet (UV) model onto an EFT makes manifest the notion of separating scales. Renormalization Group (RG) techni...

An introduction to methods of effective field theory is given. Examples are presented, including Rayleigh scattering from nonrelativistic quantum mechnics, chiral perturbation theory/QCD as well as electromagnetic and weak interactions of nucleons.

This is a lightly edited version of the talk given on September 30, 2020 to inaugurate the international seminar series {\it All Things EFT}. It reviews some of the early history of effective field theories, and concludes with a discussion of the implications of effective field theory for future discovery.

I discuss effective field theories for heavy bound systems, particularly bound systems involving two heavy quarks. The emphasis is on the relevant concepts and on interesting physical applications and results.

A new attempt is demonstrated that QFTs can be UV finite if they are viewed as the low energy effective theories of a fundamental underlying theory (that is complete and well-defined in all respects) according to the modern standard point of view. This approach works for any interaction model and space-time dimension. It is much simpler in principle and in technology comparing to any known renormalization program.Unlike the known renormalization methods, the importance of the...

A pedagological introduction to effective field theory is presented.

We summarize recent progress in the development, application, and understanding of effective field theories and highlight promising directions for future research. This Report is prepared as the TF02 "Effective Field Theory" topical group summary for the Theory Frontier as part of the Snowmass 2021 process.