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

F. Hiroshima; K. R. Ito

doi:10.1142/S0219025704001761

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

F. Hiroshima, K. R. Ito

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	547-571
Number of pages	25
Journal	Infinite Dimensional Analysis, Quantum Probability and Related Topics
Volume	7
Issue number	4
DOIs	https://doi.org/10.1142/S0219025704001761
Publication status	Published - Dec 2004
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Statistics and Probability
Mathematical Physics
Applied Mathematics

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10.1142/S0219025704001761

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abstract = "A one-parameter symplectic group {et{\^A}} 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 {et{\^A}}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({\^A}) and a local exponent ∫0tτ{\^A}(s)ds with a real-valued function τ{\^A}(·) such that Ut = ei∫0t τ {\^A} (s)ds e itΔ({\^A}).",

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year = "2004",

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doi = "10.1142/S0219025704001761",

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T1 - Local exponents and infinitesimal generators of canonical transformations on boson fock spaces

AU - Hiroshima, F.

AU - Ito, K. R.

PY - 2004/12

Y1 - 2004/12

N2 - A one-parameter symplectic group {etÂ} 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 {etÂ}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 Â (s)ds e itΔ(Â).

AB - A one-parameter symplectic group {etÂ} 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 {etÂ}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 Â (s)ds e itΔ(Â).

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

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