A Mathematical Definition of Path Integrals on Symplectic Manifolds

2024/06/20 by Lackman, Joshua
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2406.14547

Abstract

We give a mathematical definition of some path integrals, emphasizing those relevant to the quantization of symplectic manifolds (and more generally, Poisson manifolds) \unicodex2013 in particular, the coherent state path integral. We show that Kähler manifolds provide many computable examples and we emphasize those whose Bergman kernel is constant along the diagonal.

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