Weyl quantization and metaplectic representation
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Abstract
The formal expansion defining the twisted exponential of an element of the Lie algebra ℋ n □ (⊕ n Sp(2, ℝ)) can be summed and this result is used to explicitly obtain the classical function ut corresponding to an evolution operator associated to a quantum Hamiltonian belonging to the above mentioned Lie algebra.
Then, by applying the Weyl quantization procedure to ut we get a representation of the group Wn □ (⊕ n Sp(2, ℝ)) in terms of integral operators, the kernels of which are expressed by means of the classical action. The family ut being only locally defined, it must be considered as a distribution on the classical phase space in order to get the metaplectic representation.
Keywords
Statistical Physic Phase Space Group Theory Integral Operator Classical Function
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© D. Reidel Publishing Company 1977