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## Statistical field theory: Perturbative expansion

*Jean Zinn-Justin*

### in Phase Transitions and Renormalization Group

- Published in print:
- 2007
- Published Online:
- January 2010
- ISBN:
- 9780199227198
- eISBN:
- 9780191711107
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227198.003.0012
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the perturbative calculation of correlation or vertex functions expressed in terms of field (functional) integrals. The successive contributions to the perturbative expansion ... More

## Perturbative renormalization group: Explicit calculations

*Jean Zinn-Justin*

### in Phase Transitions and Renormalization Group

- Published in print:
- 2007
- Published Online:
- January 2010
- ISBN:
- 9780199227198
- eISBN:
- 9780191711107
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227198.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter uses the assumptions introduced in Chapter 9 to show that it is indeed possible to find a non-Gaussian fixed point in dimension d = 4 - e, both in models with reflection and rotation ... More

## QUANTUM EVOLUTION AND SCATTERING MATRIX

*Jean Zinn-Justin*

### in Path Integrals in Quantum Mechanics

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198566748
- eISBN:
- 9780191717994
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566748.003.0009
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter shows how scattering problems are formulated in the framework of path integrals. In quantum mechanics, the state of an isolated system evolves under the action of a unitary operator, as ... More

## PATH INTEGRALS: FERMIONS

*Jean Zinn-Justin*

### in Path Integrals in Quantum Mechanics

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198566748
- eISBN:
- 9780191717994
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566748.003.0007
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

The methods that have been described in previous chapters can be used to study general quantum Bose systems. They are based in a direct way on the introduction of a generating function of symmetric ... More

## The quartic tensor model

*Razvan Gurau*

### in Random Tensors

- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780198787938
- eISBN:
- 9780191829918
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198787938.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Particle Physics / Astrophysics / Cosmology

This chapter studies in detail the tensor model with an arbitrary quartic interaction. Using the Hubbard–Stratonovich intermediate field representation, the quartic model can be reformulated in terms ... More

## The perturbative expansion of tensor models

*Razvan Gurau*

### in Random Tensors

- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780198787938
- eISBN:
- 9780191829918
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198787938.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Particle Physics / Astrophysics / Cosmology

This chapter presents the perturbative expansion of invariant tensor measures in terms of Feynman graphs. It is shown that, assuming that the perturbation and the Gaussian part scale at the same rate ... More

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