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## High temperature expansions for magnets at H = 0

*Barry M. McCoy*

### in Advanced Statistical Mechanics

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199556632
- eISBN:
- 9780191723278
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199556632.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the results of high temperature series expansions for classical n component spin models with nearest neighbor interactions for two and three dimensions. In dimension three this ... More

## The Standard Model. Anomalies

*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/9780198509233.003.0020
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 19 discussed the structure and the formal properties of non-abelian gauge theories. This chapter applies this formalism to the description of some general properties of the Standard Model of ... More

## The Principles of Renormalisation

*J. Iliopoulos and T.N. Tomaras*

### in Elementary Particle Physics: The Standard Theory

- Published in print:
- 2021
- Published Online:
- December 2021
- ISBN:
- 9780192844200
- eISBN:
- 9780191926983
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780192844200.003.0015
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

Loop diagrams often yield ultraviolet divergent integrals. We introduce the concept of one-particle irreducible diagrams and develop the power counting argument which makes possible the ... More

## O(N) vector model in the ordered phase: Goldstone modes

*Jean Zinn-Justin*

### in From Random Walks to Random Matrices

- Published in print:
- 2019
- Published Online:
- August 2019
- ISBN:
- 9780198787754
- eISBN:
- 9780191829840
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198787754.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 10 examines the case of the spontaneous breaking of a continuous symmetry. When there is spontaneous symmetry breaking, the correlation length diverges at all temperatures in the ordered ... More

## The Strong Interactions

*J. Iliopoulos and T.N. Tomaras*

### in Elementary Particle Physics: The Standard Theory

- Published in print:
- 2021
- Published Online:
- December 2021
- ISBN:
- 9780192844200
- eISBN:
- 9780191926983
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780192844200.003.0021
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

For many years strong interactions had a well-deserved reputation for complexity. Their apparent strength rendered perturbation theory inapplicable. However, in the late 1960s a series of experiments ... More

## Quantum chromodynamics: A non-Abelian gauge theory

*Jean Zinn-Justin*

### in From Random Walks to Random Matrices

- Published in print:
- 2019
- Published Online:
- August 2019
- ISBN:
- 9780198787754
- eISBN:
- 9780191829840
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198787754.003.0013
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 13 is devoted to some aspects of quantum chromodynamics (QCD), the part of the Standard Model of particle physics responsible for strong interactions and based on an SU(3) gauge symmetry (the ... More

## The renormalization group

*Tom Lancaster and Stephen J. Blundell*

### in Quantum Field Theory for the Gifted Amateur

- Published in print:
- 2014
- Published Online:
- June 2014
- ISBN:
- 9780199699322
- eISBN:
- 9780191779435
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199699322.003.0035
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

The renormalization group is introduced in this chapter. Examples treated include asymptotic freedom, Anderson localization, and the Kosterlitz–Thouless transition.

## Large-momentum behaviour in quantum field theory (QFT)

*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/9780198834625.003.0024
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Renormalization group (RG) equations are used to characterize the large momentum behaviour of renormalized quantum field theories (QFT), assuming implicitly that such a universal large momentum ... More

## The Existence of Field Theories beyond the Perturbation Expansion

*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/9780198788393.003.0024
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

The standard model of fundamental interactions. A brief summary of the phenomenology of weak interactions. The construction of the electroweak theory and its experimental consequences. The deep ... More

## More on the Fundamental Forces and Their “Carriers”

*Alvaro De Rújula*

### in Enjoy Our Universe: You Have No Other Choice

- Published in print:
- 2018
- Published Online:
- February 2020
- ISBN:
- 9780198817802
- eISBN:
- 9780191859366
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198817802.003.0007
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

A discussion of the “carriers” of the basic forces of nature and the way they “work.” Electrical charges and their interaction with photons (QED). Gravitons and the identity of inertial 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:

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

## Epilogue and future work

*Massimiliano Di Ventra*

### in MemComputing: Fundamentals and Applications

- Published in print:
- 2022
- Published Online:
- March 2022
- ISBN:
- 9780192845320
- eISBN:
- 9780191937521
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780192845320.003.0013
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This Chapter summarizes the book’s main points and offers ideas for further research in the field of MemComputing. It also makes connections with several physical theories such as Renormalization ... More

## One-loop divergences

*Iosif L. Buchbinder and Ilya L. Shapiro*

### in Introduction to Quantum Field Theory with Applications to Quantum Gravity

- Published in print:
- 2021
- Published Online:
- April 2021
- ISBN:
- 9780198838319
- eISBN:
- 9780191874666
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198838319.003.0014
- Subject:

This chapter focuses on one-loop calculations and related issues such as practical renormalization and the derivation of beta functions. The general result for the one-loop divergences from chapter ... More

## Quantum Chromodynamics

*Michael E. Peskin*

### in Concepts of Elementary Particle Physics

- Published in print:
- 2019
- Published Online:
- November 2019
- ISBN:
- 9780198812180
- eISBN:
- 9780191850301
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198812180.003.0011
- Subject:

This chapter introduces non-Abelian gauge symmetry and the associated field equations for spin-1 particles. It proposes the gauge theory Quantum Chromodynamics as the theory of the strong ... More

## A few solvable two-dimensional quantum field theories (QFT)

*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/9780198834625.003.0030
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The chapter is devoted to several two-dimensional quantum field theories (QFT), whose properties can be determined by non-perturbative methods. The Schwinger model, a model of two-dimensional quantum ... More

##
Generalized non-linear *σ*-models in two dimensions

*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/9780198834625.003.0029
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter describes the formal properties, and discusses the renormalization, of quantum field theories (QFT) based on homogeneous spaces: coset spaces of the form G/H, where G is a compact Lie ... More

## Gross–Neveu–Yukawa and Gross–Neveu models

*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/9780198834625.003.0020
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In this chapter, a model is considered that can be defined in continuous dimensions, the Gross– Neveu–Yukawa (GNY) model, which involves N Dirac fermions and one scalar field. The model has a ... More

## Particle physics II

*Ian R. Kenyon*

### in Quantum 20/20: Fundamentals, Entanglement, Gauge Fields, Condensates and Topology

- Published in print:
- 2019
- Published Online:
- November 2019
- ISBN:
- 9780198808350
- eISBN:
- 9780191846052
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198808350.003.0019
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Particle Physics / Astrophysics / Cosmology

Quantum chromodynamics the quantum gauge theory of strong interactions is presented: SU(3) being the (colour) symmetry group. The colour content of strongly interacting particles is described. ... More

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