Open AccessCanonical Linear Transformation on Fock Space with an Indefinite Metric
Author(s) -
Keiichi R. Ito
Publication year - 1978
Publication title -
publications of the research institute for mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.786
H-Index - 39
eISSN - 1663-4926
pISSN - 0034-5318
DOI - 10.2977/prims/1195189075
Subject(s) - mathematics , fock space , bijection , hilbert space , sesquilinear form , linear map , unitary operator , polar decomposition , bounded function , combinatorics , pure mathematics , bounded operator , hermitian matrix , mathematical analysis , quantum mechanics , polar , physics
We first construct a Fock space with an indefinite metric =( , T), where T is a unitary and Hermitian operator. We define a T-selfadjoint (Segal's) field F?(f) which obeys the canonical commutation relations (CCR) with an indefinite metric. We consider a transformation 349-2 (T = real linear) which leaves the CCR invariant. We investigate the implementability of T by an operator on the Fock space.
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