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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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