A uniqueness result for the segal quantization of a classical system with symmetries
In the Segal approach, a classical system with symmetries can be quantized in a straightforward way when a complexification operator exists for both the symplectic space that describes the phase space and the symplectic transformations that represent the symmetry group of the system. If such group fulfils a real irreducibility condition, the complexification operator is unique . Two applications, to finite dimensional systems and to free Bose fields, arc briefly described.
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