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## Introduction to Renormalization Theory. Renormalization Group Equations

*JEAN ZINN-JUSTIN*

### in Quantum Field Theory and Critical Phenomena

- Published in print:
- 2002
- Published Online:
- January 2010
- ISBN:
- 9780198509233
- eISBN:
- 9780191708732
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509233.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the essential steps of the proof of the renormalizability of a simple scalar field theory: the φ4 field theory in d = 4 dimensions. However, all the fundamental difficulties of ... More

## Non-perturbative heavy quark effective theory

*Rainer Sommer*

### in Modern Perspectives in Lattice QCD: Quantum Field Theory and High Performance Computing: Lecture Notes of the Les Houches Summer School: Volume 93, August 2009

- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199691609
- eISBN:
- 9780191731792
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199691609.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter describes a heuristic derivation of the HQET Lagrangian from continuum QCD and discusses the renormalization of the effective field theory. A lattice discretization is introduced ... More

## Dynamics VII: Interacting fields: general aspects

*Anthony Duncan*

### in The Conceptual Framework of Quantum Field Theory

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199573264
- eISBN:
- 9780191743313
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573264.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter deals with the intricacies of interacting field theories, emphasizing very general aspects common to all local quantum field theories (LQFTs). The basic concept here is that of the ... More

## A First Glance at Renormalisation and Symmetry

*Laurent Baulieu, John Iliopoulos, and Roland Sénéor*

### in From Classical to Quantum Fields

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780198788393
- eISBN:
- 9780191830310
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198788393.003.0017
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

The fate of the classical symmetries in a quantum field theory after renormalisation. Global symmetries versus gaugec symmetries. The Adler–Bell–Jackiw anomaly. The breaking of scale invariance and ... More

## Some Consequences of the Renormalisation Group

*Laurent Baulieu, John Iliopoulos, and Roland Sénéor*

### in From Classical to Quantum Fields

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780198788393
- eISBN:
- 9780191830310
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198788393.003.0019
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

The use of the renormalisation group and the Callan–Symanzik equations in the study of the asymptotic behaviour of Green functions. The stability properties of a Lagrangian field theory. The ... More

##
Quantum field theory (QFT)—*built-in combinatorics*

*Adrian Tanasa*

### in Combinatorial Physics: Combinatorics, Quantum Field Theory, and Quantum Gravity Models

- Published in print:
- 2021
- Published Online:
- May 2021
- ISBN:
- 9780192895493
- eISBN:
- 9780191914973
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780192895493.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

We briefly exhibit in this chapter the mathematical formalism of QFT, which actually has a non-trivial combinatorial backbone. The QFT setting can be understood as a quantum description of particles ... More

## Fermionic QFT, Grassmann calculus, and combinatorics

*Adrian Tanasa*

### in Combinatorial Physics: Combinatorics, Quantum Field Theory, and Quantum Gravity Models

- Published in print:
- 2021
- Published Online:
- May 2021
- ISBN:
- 9780192895493
- eISBN:
- 9780191914973
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780192895493.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In the first section of this chapter, we use Grassmann calculus, used in fermionic QFT, to give, first a reformulation of the Lingström–Gesse–Viennot lemma proof. We further show that this proof ... More

## Renormalization of local polynomials. Short-distance expansion (SDE)

*Jean Zinn-Justin*

### in Quantum Field Theory and Critical Phenomena: Fifth Edition

- Published in print:
- 2021
- Published Online:
- June 2021
- ISBN:
- 9780198834625
- eISBN:
- 9780191872723
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198834625.003.0011
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses two related topics: the renormalization of local polynomials (or local operators) of the field, and the short-distance expansion (SDE) of the product of local operators, in ... More

## Introduction to renormalization theory and renormalization group (RG)

*Jean Zinn-Justin*

### in Quantum Field Theory and Critical Phenomena: Fifth Edition

- Published in print:
- 2021
- Published Online:
- June 2021
- ISBN:
- 9780198834625
- eISBN:
- 9780191872723
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198834625.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

A straightforward construction of a local, relativistic quantum field theory (QFT) leads to ultraviolet (UV) divergences and a QFT has to be regularized by modifying its short-distance or large ... More

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