Local exponents and infinitesimal generators of canonical transformations on boson fock spaces

Fumio Hiroshima, K. R. Ito

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

A one-parameter symplectic group {e} tεℝ derives proper canonical transformations indexed by t on a Boson-Fock space. It has been known that the unitary operator Ut implementing such a proper canonical transformation gives a projective unitary representation of {e}tεℝ on the Boson-Fock space and that Ut can be expressed as a normal-ordered form. We rigorously derive the self-adjoint operator Δ(Â) and a local exponent ∫0tτÂ(s)ds with a real-valued function τÂ(·) such that Ut = ei∫0t τ  (s)ds e itΔ(Â).

Original languageEnglish
Pages (from-to)547-571
Number of pages25
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Volume7
Issue number4
DOIs
Publication statusPublished - Dec 1 2004

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Bosons
Canonical Transformation
Infinitesimal Generator
Fock Space
generators
bosons
Exponent
exponents
operators
Unitary Operator
Symplectic Group
Unitary Representation
Self-adjoint Operator
Form

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Mathematical Physics
  • Applied Mathematics

Cite this

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