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The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

Helmut Hofmann

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198504016
eISBN:
9780191708480
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504016.001.0001
Subject:
Physics, Nuclear and Plasma Physics

This book offers a survey of nuclear physics at low energies and discusses similarities to mesoscopic systems. It addresses systems at finite excitations of the internal degrees of freedom where ... More


Quantum Field Theory: Functional Methods and Perturbation Theory

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/9780198509233.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter proceeds with the study of local, relativistic quantum field theory. It first discusses the neutral self-coupled scalar field φ(x) introduced in Section 6.6.1. An important example is ... More


Quantum Evolution: From Particles To Fields

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/9780198509233.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

To calculate scattering S-matrix elements, quantities relevant to Particle Physics, it is necessary to consider instead the quantum evolution operator in real time. This chapter begins by deriving ... More


FUNCTIONAL INTEGRALS

Robert M. Mazo

in Brownian Motion: Fluctuations, Dynamics, and Applications

Published in print:
2008
Published Online:
January 2010
ISBN:
9780199556441
eISBN:
9780191705625
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556441.003.0006
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses a different kind of integral, functional integrals or Wiener integrals. The idea of an integral over a space of functions is introduced. The way to define such an integral ... More


Path And Functional Integrals In Quantum Statistical Physics

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/9780198509233.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Hamiltonians in quantum mechanics can be expressed in terms of creation and annihilation operators, instead of the more usual position and momentum operators, a method well adapted to the study of ... More


The temporal ultraviolet limit

Tadeusz Balaban, Joel Feldman, Horst Knörrer, and Eugene Trubowitz

in Quantum Theory from Small to Large Scales: Lecture Notes of the Les Houches Summer School: Volume 95, August 2010

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199652495
eISBN:
9780191741203
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199652495.003.0002
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter is concerned with the first, relatively small, step in a program whose long-term goal is the mathematically rigorous construction of a standard model of a gas of bosons. Even this first ... More


Functional Calculus for C-Number and Grassmann Fields

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

in Phase Space Methods for Degenerate Quantum Gases

Published in print:
2014
Published Online:
April 2015
ISBN:
9780199562749
eISBN:
9780191747311
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199562749.003.0011
Subject:
Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

This chapter presents the basic mathematical tools required for extending the phase space method involving phase space variables for separate modes to a phase space method involving field functions ... More


Relativistic Fermions

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/9780198509233.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses boson field theories, occasionally considering theories with fermions, in particular, when the fermion nature of fields plays an essential role. It analyzes the free action for ... More


Functional integration: From path to field integrals

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/9780198787754.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 2 is rather descriptive and introduces the notion of functional (path and field) integrals, for boson (the holomorphic formalism) as well as fermion systems (this necessitates the ... More


Level densities and nuclear thermometry

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/9780198504016.003.0010
Subject:
Physics, Nuclear and Plasma Physics

Based on the Darwin-Fowler approximation various models for the many-body level density Ω are introduced, critically examined, and confronted with empirical parameterizations. This concerns both the ... More


Functional integrals

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/9780198838319.003.0007
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter presents an alternative approach to the quantization of fields, an approach that will be critically important for the development of quantum field theory in curved space, which is the ... More


The essential role of functional integrals in modern physics

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/9780198787754.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 3 illustrates by a number of examples the essential role of functional integrals in physics. For example, the path integral representation of quantum mechanics explains why many basic ... More


Distribution Functionals in Quantum Atom Optics

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

in Phase Space Methods for Degenerate Quantum Gases

Published in print:
2014
Published Online:
April 2015
ISBN:
9780199562749
eISBN:
9780191747311
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199562749.003.0012
Subject:
Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

This chapter formally presents the representation of the quantum density operator by phase space distribution functionals of phase space fields, leading to expressions for quantum correlation ... More


Functional Integrals and Probabilistic Amplitudes

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/9780198788393.003.0008
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

Functional integrals and probabilistic amplitudes. Brief historical notes. The reconstruction of quantum mechanics from path integrals. The Feynman formulation. Definition and properties of the ... More


Grassmann numbers: coherent states and the path integral for fermions

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/9780199699322.003.0029
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter introduces a new type of mathematical object: Grassmann numbers. These anticommute and can be used to describe fermions. It shows how to construct a fermion path integral using Grassmann ... More


Quantum Field Theory for the Gifted Amateur

Tom Lancaster and Stephen J. Blundell

Published in print:
2014
Published Online:
June 2014
ISBN:
9780199699322
eISBN:
9780191779435
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199699322.001.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Quantum field theory is arguably the most far-reaching and beautiful physical theory ever constructed, with aspects more stringently tested and verified to greater precision than any other theory in ... More


Quantum fields in curved spacetime: renormalization

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/9780198838319.003.0013
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

In this chapter, which forms the central chapter of Part II, the effective action of quantum matter fields in curved spacetime is formulated in terms of functional integrals. A qualitative, albeit ... More


Instantons in quantum mechanics (QM)

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/9780198834625.003.0037
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Perturbative expansion can be generated by calculating Euclidean functional integrals by the steepest descent method always looking, in the absence of external sources, for saddle points in the form ... More


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