The ground state energy of a quantum system is extracted from the large imaginary-time limit of the phase space integral of the star exponential of the Hamiltonian, a reformulation of the trace formula.
Deformation Quantization and Wigner Functions
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abstract
We review the Weyl-Wigner formulation of quantum mechanics in phase space. We discuss the concept of Narcowich-Wigner spectrum and use it to state necessary and sufficient conditions for a phase space function to be a Wigner distribution. Based on this formalism we analize the modifications introduced by the presence of boundaries. Finally, we discuss the concept of environment-induced decoherence in the context of the Weyl-Wigner approach.
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The Feynman-Kac formula in deformation quantization
The ground state energy of a quantum system is extracted from the large imaginary-time limit of the phase space integral of the star exponential of the Hamiltonian, a reformulation of the trace formula.