A uniqueness result in the Segal–Weinless approach to linear Bose fields
- 1 August 1979
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 20 (8) , 1712-1713
- https://doi.org/10.1063/1.524253
Abstract
We prove a theorem, which, while it fits naturally into the Segal–Weinless approach to quantization seems to have been overlooked in the literature: Let (D,σ) be a symplectic space, and T (t) a one parameter group of symplectics on (D,σ). Let (H, 2Im〈⋅ ‖ ⋅〉) be a complex Hilbert space considered as a real symplectic space, and U(t) a one‐parameter unitary group on H with strictly positive energy. Suppose there is a linear symplectic map K from D to H with dense range, intertwining T (t) and U(t). Then K is unique up to unitary equivalence.Keywords
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