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## 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

## Algebraic Preliminaries

*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/9780198509233.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter reviews algebraic identities about gaussian integrals, in particular Wick's theorem, a result also relevant for gaussian probability distributions. It discusses the steepest descent ... More

## Clifford, or Geometric, Algebra

*Jayme Vaz and Roldão da Rocha*

### in An Introduction to Clifford Algebras and Spinors

- Published in print:
- 2016
- Published Online:
- August 2016
- ISBN:
- 9780198782926
- eISBN:
- 9780191826146
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198782926.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In this chapter, the so-called geometric algebras, or Clifford algebras, are introduced, with special attention to the universal Clifford algebras. As well as providing the standard definition of a ... More

## Exterior Algebra and Grassmann Algebra

*Jayme Vaz and Roldão da Rocha*

### in An Introduction to Clifford Algebras and Spinors

- Published in print:
- 2016
- Published Online:
- August 2016
- ISBN:
- 9780198782926
- eISBN:
- 9780191826146
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198782926.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In this chapter, exterior algebras and Grassmann algebras are discussed. In particular, their morphisms, inherited from the tensor algebra, are presented in a general framework. In some texts, the ... More

## Fermions and Functional Formalism

*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/9780198788393.003.0011
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

The introduction of spinor fields and the problem of the positivity of the energy. Need for anti-commutators. Calculus in a Grassmannian manifold, the Berezin integral. Clifford algebras. Quantum ... More

## An Introduction to Clifford Algebras and Spinors

*Jayme Vaz, Jr. and Roldão da Rocha, Jr.*

- Published in print:
- 2016
- Published Online:
- August 2016
- ISBN:
- 9780198782926
- eISBN:
- 9780191826146
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198782926.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This book is unique in the literature on spinors and Clifford algebras in that it is accessible to both students and researchers while maintaining a formal approach to these subjects. Besides ... More

## Phase Space Methods for Degenerate Quantum Gases

*Bryan J. Dalton, John Jeffers, and Stephen M. Barnett*

- Published in print:
- 2014
- Published Online:
- April 2015
- ISBN:
- 9780199562749
- eISBN:
- 9780191747311
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199562749.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

Recent experimental progress has enabled cold atomic gases to be studied at nanokelvin temperatures, creating new states of matter where quantum degeneracy occurs—Bose–Einstein condensates and ... More

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