Chapter 16. Density Operators for Fermions

  1. Roy J. Glauber

Published Online: 19 JAN 2007

DOI: 10.1002/9783527610075.ch16

Quantum Theory of Optical Coherence: Selected Papers and Lectures

Quantum Theory of Optical Coherence: Selected Papers and Lectures

How to Cite

Glauber, R. J. (2006) Density Operators for Fermions, in Quantum Theory of Optical Coherence: Selected Papers and Lectures, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527610075.ch16

Author Information

  1. Lyman Laboratory, Harvard University Cambridge, MA 02138, USA

  1. Reprinted with permission from K. E. Cahill, R. J. Glauber, Phys. Rev. A 59, 1538–1555 (1999). Copyright 2006 by the American Physical Society.

Publication History

  1. Published Online: 19 JAN 2007
  2. Published Print: 15 DEC 2006

ISBN Information

Print ISBN: 9783527406876

Online ISBN: 9783527610075

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Keywords:

  • quantum theory;
  • optical coherence;
  • density operators;
  • fermions;
  • notation;
  • Grassmann calculus;
  • delta functions;
  • Fourier transforms;
  • operator expansions;
  • s-ordered expansions;
  • quasiprobability distributions;
  • P representation;
  • correlation functions;
  • chaotic states;
  • fermion field

Summary

This chapter contains sections titled:

  • Introduction

  • Notation

  • Coherent States for Fermions

    • Displacement Operators

    • Coherent States

    • Intrinsic Descriptions of Fermionic States

  • Grassmann Calculus

    • Differentiation

    • Even and Odd Functions

    • Product Rule

    • Integration

    • Integration by Parts

    • Completeness of the Coherent States

    • Completeness of the Displacement Operators

  • Operators

    • The Identity Operator

    • The Trace

    • Physical States and Operators

    • Physical Density Operators

  • δ Functions and Fourier Transforms

  • Operator Expansions

  • Characteristic Functions

    • The s-Ordered Characteristic Function

  • s-Ordered Expansions for Operators

  • Quasiprobability Distributions

  • Mean Values of Operators

  • P Representation

  • Correlation Functions for Fermions

  • Chaotic States of the Fermion Field

  • Correlation Functions for Chaotic Field Excitations

  • Fermion-Counting Experiments

  • Some Elementary Examples

    • The Vacuum State

    • A Physical Two-Mode Density Operator

  • References