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Formal means

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/9780198504016.003.0026
Subject:
Physics, Nuclear and Plasma Physics

This chapter elucidates various mathematical formulas. Based on expressions for Gaussian integrals in one and many dimensions, the methods of stationary phase and steepest descent are deduced, ... More


Quantum Many-Particle Systems and Second Quantization

Hans-Peter Eckle

in Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz

Published in print:
2019
Published Online:
September 2019
ISBN:
9780199678839
eISBN:
9780191878589
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199678839.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

Chapter 2 provides a review of pertinent aspects of the quantum mechanics of systems composed of many particles. It focuses on the foundations of quantum many-particle physics, the many-particle ... More


Interacting boson systems

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/9780199227259.003.03
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces a quantum field theory for interacting boson systems. It develops a mean-field theory to study the superfluid phase. A path integral formulation is then developed to re-derive ... More


Statistics and Collective Properties of Frenkel Excitons

Vladimir M. Agranovich

in Excitations in Organic Solids

Published in print:
2008
Published Online:
January 2009
ISBN:
9780199234417
eISBN:
9780191715426
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199234417.003.0015
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter describes the approximate second quantization and approximate transition to boson picture. Using exact transformation from paulions to bosons, the collective properties of an ideal ... More


Identical Particles: Individuation and Modality 1

Bas C. van Fraassen

in Quantum Mechanics: An Empiricist View

Published in print:
1991
Published Online:
November 2003
ISBN:
9780198239802
eISBN:
9780191597466
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198239807.003.0012
Subject:
Philosophy, Philosophy of Science

This chapter aims to place the discussion of holism in quantum theory generally and of the problem of identical particles and quantum statistics specifically in the context of general philosophy. ... More


Green Functions

Nikolai B. Kopnin

in Theory of Nonequilibrium Superconductivity

Published in print:
2001
Published Online:
January 2010
ISBN:
9780198507888
eISBN:
9780191709722
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507888.003.02
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces the second quantization formalism based on Schrödinger and Heisenberg operators. It defines the temperature and real-time Green functions for Bose and Fermi particles and ... More


Excitations in Organic Solids

Vladimir Agranovich

Published in print:
2008
Published Online:
January 2009
ISBN:
9780199234417
eISBN:
9780191715426
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199234417.001.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

This book details the studies of the properties of electronic and vibrational excitations in organic solids. It brings together most of the theory in this field together with many illustrations of ... More


Identical particles

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/9780198749349.003.0025
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter discusses the case of a many-body system of identical particles. It considers the consequencies of the symmetry of the Hamiltonian under particle permutations in this case. It discusses ... More


Identical particles; Second quantization

Victor Galitski, Boris Karnakov, Vladimir Kogan, and Victor Galitski, Jr.

in Exploring Quantum Mechanics: A Collection of 700+ Solved Problems for Students, Lecturers, and Researchers

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199232710
eISBN:
9780191774973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232710.003.0010
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter analyzes issues that deal with quantum statistics (symmetry of wavefunctions); elements of the second quantization formalism (the occupation-number representation); and the simplest ... More


Dynamics IV: Aspects of locality: clustering, microcausality, and analyticity

Anthony Duncan

in The Conceptual Framework of Quantum Field Theory

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199573264
eISBN:
9780191743313
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573264.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 5 discussed two possible approaches to constructing a relativistically invariant theory of particle scattering. The first attempt — a frontal assault in which one directly writes down for ... 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


Simple harmonic oscillators

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/9780199699322.003.0003
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

The simple harmonic oscillator is well known from basic quantum physics as an elementary model of an oscillating system. The chapter solves this simple model using creation and annihilation operators ... More


Making second quantization work

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/9780199699322.003.0005
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter considers how to build single-particle operators out of creation and annihilation operators, and this already gives enough information to discuss the tight-binding model of solid state ... More


Identical Particles and Second Quantization: Occupation Number Representation

Norman J. Morgenstern Horing

in Quantum Statistical Field Theory: An Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198791942
eISBN:
9780191834165
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198791942.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized ... More


π-electron theories of conjugated polymers

William Barford

in Electronic and Optical Properties of Conjugated Polymers

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199677467
eISBN:
9780191757402
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199677467.003.0002
Subject:
Physics, Condensed Matter Physics / Materials

Semi-empirical π‐electron theories of conjugated polymers are introduced, starting from the fundamentals of the Born-Oppenheimer approximation and sp-hybridization. The models described include the ... More


States and Operators

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/9780199562749.003.0002
Subject:
Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

This chapter sets out the second-quantisation treatment for systems of identical bosons or fermions. Key features such as the symmetrisation principle and super-selection rules are presented. ... More


Occupation number representation

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/9780199699322.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter changes our viewpoint and get rid of wave functions entirely and develops the occupation number representation. The chapter shows that bosons are described by commuting operators and ... More


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