### 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}^{t}τ_{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 |
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Pages (from-to) | 547-571 |

Number of pages | 25 |

Journal | Infinite Dimensional Analysis, Quantum Probability and Related Topics |

Volume | 7 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 1 2004 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

**Local exponents and infinitesimal generators of canonical transformations on boson fock spaces.** / Hiroshima, Fumio; Ito, K. R.

Research output: Contribution to journal › Article

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TY - JOUR

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

AU - Hiroshima, Fumio

AU - Ito, K. R.

PY - 2004/12/1

Y1 - 2004/12/1

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).

UR - http://www.scopus.com/inward/record.url?scp=12144250196&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=12144250196&partnerID=8YFLogxK

U2 - 10.1142/S0219025704001761

DO - 10.1142/S0219025704001761

M3 - Article

VL - 7

SP - 547

EP - 571

JO - Infinite Dimensional Analysis, Quantum Probability and Related Topics

JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics

SN - 0219-0257

IS - 4

ER -