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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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