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理论物理通讯：英文版

Coherent State Projection Operator Representation of Symplectic Transformations as a Loyal Representation of Symplectic Group

Fan, Hong-Yi, Chen, Jun-Hua

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

We find that the coherent state projection operator representation of symplectic transformation constitutesa loyal group representation of symplectic group. The result of successively applying squeezing operators on numberstate can be easily derived.

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For the two-mode fermionic squeezing operators we find that their coherent state projection operator representation make up a loyal representation, which is homomorphic to an SO(4) group, though the fermionic coherent states are not mutual orthogonal. Thus the result of successively operating with many fermionic squeezing operators on a state can be equivalent to a single operation. The fermionic squeezing operators are mappings of orthogonal transformations in Grassmann number pseudo-classical space in the fermionic coherent state representation.