Coherent state map quantization in a Hermitian-like setting

Beltiţă, Daniel; Galé, Jośe E.

doi:10.1016/j.geomphys.2015.02.005

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Parallel Translation and Transition Probability Amplitudes1

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“…also D. Beltiţȃ and J.E. Galé [74], R. Coquereaux and A. Jadczyk [75], M. Englis [76], V.V. Kisil [77], M.I.…”

Section: Parallel Translation and Transition Probability Amplitudesmentioning

confidence: 99%

Weighted Bergman Kernels and Mathematical Physics

Barletta

Dragomir

Esposito

2020

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We review several results in the theory of weighted Bergman kernels. Weighted Bergman kernels generalize ordinary Bergman kernels of domains Ω ⊂ C n but also appear locally in the attempt to quantize classical states of mechanical systems whose classical phase space is a complex manifold, and turn out to be an efficient computational tool that is useful for the calculation of transition probability amplitudes from a classical state (identified to a coherent state) to another. We review the weighted version (for weights of the form γ = | φ | m on strictly pseudoconvex domains Ω = { φ < 0 } ⊂ C n ) of Fefferman’s asymptotic expansion of the Bergman kernel and discuss its possible extensions (to more general classes of weights) and implications, e.g., such as related to the construction and use of Fefferman’s metric (a Lorentzian metric on ∂ Ω × S 1 ). Several open problems are indicated throughout the survey.

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“…also D. Beltiţȃ and J.E. Galé [74], R. Coquereaux and A. Jadczyk [75], M. Englis [76], V.V. Kisil [77], M.I.…”

Section: Parallel Translation and Transition Probability Amplitudesmentioning

confidence: 99%