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Path Integrals and Quantum Anomalies

Kazuo Fujikawa and Hiroshi Suzuki

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198529132
eISBN:
9780191712821
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529132.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book provides an introduction to the path integral formulation of quantum field theory and its applications to the analyses of symmetry breaking by the quantization procedure. This symmetry ... More


Path Integrals in Quantum Mechanics

Jean Zinn-Justin

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198566748
eISBN:
9780191717994
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566748.001.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

Path integrals are mathematical objects that can be considered as generalizations to an infinite number of variables, represented by paths, of usual integrals. They share the algebraic properties of ... More


CONCLUDING REMARKS

Kazuo Fujikawa and Hiroshi Suzuki

in Path Integrals and Quantum Anomalies

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198529132
eISBN:
9780191712821
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529132.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter considers a possible intuitive explanation of quantum breaking of symmetries as well as the subjects which are not discussed in the main chapters, such as the descent formula for gauge ... More


THE FEYNMAN PATH INTEGRAL AND SCHWINGER'S ACTION PRINCIPLE

Kazuo Fujikawa and Hiroshi Suzuki

in Path Integrals and Quantum Anomalies

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198529132
eISBN:
9780191712821
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529132.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter provides a brief introduction to the basics of quantum field theory. The basic ideas of Feynman path integrals and Schwinger’s action principle, a knowledge of which is required to ... More


Path Integral Formulation of Quantum Mechanics

Xiao-Gang Wen

in Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons

Published in print:
2007
Published Online:
February 2010
ISBN:
9780199227259
eISBN:
9780191713019
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227259.003.02
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces path integral and various correlation functions at zero and non-zero temperatures to study interacting quantum systems. Semi-classical approximation and instanton effects are ... More


Functional integrals

Helmut Hofmann

in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198504016
eISBN:
9780191708480
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504016.003.0024
Subject:
Physics, Nuclear and Plasma Physics

This chapter presents a short review of path integrals in quantum mechanics. This is followed by a detailed discussion of the evaluation of the semi-classical propagator, involving quadratic ... More


PATH INTEGRALS IN QUANTUM MECHANICS

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/9780198566748.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter constructs the path integral associated with the statistical operator e -βH in the case of Hamiltonians of the simple form p2/2m + V (q). The path ... More


PATH INTEGRALS AND HOLOMORPHIC FORMALISM

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/9780198566748.003.0006
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter introduces the holomorphic representation of quantum mechanics, because it allows a study of the properties of boson systems both from the point of view of evolution and of quantum ... More


Euclidean Path Integrals In Quantum Mechanics

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/9780198509233.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter focuses on Quantum Mechanics and Quantum Field Theory in a euclidean formulation. This means that, in general, it discusses the matrix elements of the quantum statistical operator eβH ... 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


Quantum mechanics and path integrals

Efstratios Manousakis

in Practical Quantum Mechanics: Modern Tools and Applications

Published in print:
2015
Published Online:
December 2015
ISBN:
9780198749349
eISBN:
9780191813474
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198749349.003.0013
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter discusses the Feymann path-integral approach to quantum mechanics. First, it derives a path integral expression for the evolution operator. Next, it shows that the classical equations of ... More


PATH INTEGRALS IN PHASE SPACE

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/9780198566748.003.0010
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter contains a few additional results such as a definition of path integrals over phase space trajectories, and the problems generated by the quantization of lagrangians with potentials ... More


PATH INTEGRALS AND QUANTIZATION

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/9780198566748.003.0005
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter constructs path integrals for general Hamiltonians with potentials linear in the velocities, like Hamiltonians of particles in a magnetic field. Two examples are considered: a quantum ... 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


INTRODUCTION TO PATH INTEGRALS

Dante Gatteschi, Roberta Sessoli, and Jacques Villain

in Molecular Nanomagnets

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198567530
eISBN:
9780191718298
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567530.003.0007
Subject:
Physics, Condensed Matter Physics / Materials

This chapter introduces the formalism of field theory applied to tunnelling effects, including imaginary time and path integrals. The theory is then specialized by applying the path integral method ... More


Path integrals, FP method and BRS transformation

Reinhold A. Bertlmann

in Anomalies in Quantum Field Theory

Published in print:
2000
Published Online:
January 2010
ISBN:
9780198507628
eISBN:
9780191706400
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507628.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter explains the path integral formalism, specifically the Faddeev–Popov method for quantizing gauge theories and the BRS transformations. Section 3.1 presents Feynman's idea of formulating ... More


BARRIER PENETRATION: SEMI-CLASSICAL APPROXIMATION

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/9780198566748.003.0008
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

A classical particle is always reflected by a potential barrier if its energy is lower than the potential. In contrast, a quantum particle has a non-vanishing probability to tunnel through a barrier, ... More


QUANTUM THEORY OF PHOTONS AND THE PHASE OPERATOR

Kazuo Fujikawa and Hiroshi Suzuki

in Path Integrals and Quantum Anomalies

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198529132
eISBN:
9780191712821
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529132.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the essence of the quantization of the electromagnetic field and its path integral representation. The electromagnetic field is the simplest example of a gauge field, and its ... More


Covariant approaches to quantum gravity

Claus Kiefer

in Quantum Gravity: Third Edition

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199585205
eISBN:
9780191739378
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199585205.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces the important concept of the graviton. It discusses at some length linearized quantum gravity and its implications. A central role is played by path-integral quantization from ... More


Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons

Xiao-Gang Wen

Published in print:
2007
Published Online:
February 2010
ISBN:
9780199227259
eISBN:
9780191713019
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227259.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been an emergence of a new ... More


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