nLab Renormalization and Effective Field Theory

This entry is to record the reference:

• Kevin Costello:

  
  

  Renormalization and effective field theory

  
  

  Mathematical Surveys and Monographs 170

  American Mathematical Society (2011)

  doi:10.1090/surv/170

  ams:surv-170,

  book pdf,

  talk slides)

on renormalization and BV-quantization of effective quantum field theory of those quantum field theories whose action functional can be brought into “BV-CS form” $S(\phi) = \langle \phi, Q \phi\rangle + I(\phi)$.

Much of the content is based on the article

• Kevin Costello, Renormalisation and the Batalin-Vilkovisky formalism (arXiv:0706.1533)

which focuses on Chern-Simons theory, as well as

• Kevin Costello, Topological conformal field theories and gauge theories (arXiv:math/0605647)

which focuses on Yang-Mills theory.

The methods of the book are designed to allow to construct quantum field theories in the form of factorization algebras of observables (see there for more details) as discussed in

• Kevin Costello, Owen Gwilliam, Factorization algebras in perturbative quantum field theory

1) Introduction

(…)

2) Theories, Lagrangians and counterterms

• theory (physics)

• prequantum field theory

• Lagrangian

3) Field theories on $\mathbb{R}^n$

• free field theory

4) Renormalizability

• renormalization

5) Gauge theory and the Batalin-Vilkovisky formalism

• gauge theory

• BV-BRST formalism

6) Renormalizability of Yang-Mills theory

• Yang-Mills theory

Appendix: Asymptotics of graph integrals

• Feynman diagram

• path integral

category: reference