Canonical linear transformation on fock space with an indefinite metric

  title={Canonical linear transformation on fock space with an indefinite metric},
  author={K. R. Ito},
  journal={Letters in Mathematical Physics},
  • K. Ito
  • Published 1 March 1978
  • Mathematics
  • Letters in Mathematical Physics
We first construct a Fock space with an indefinite metric 〈,〉=( , Θ), where Θ is a unitary and Hermitian operator. We define a Θ-selfadjoint (Segal's) field Φϕ(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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Indefinite Inner Product Space " (Springer

  • Verlag. Berlin
  • 1973