Path Integral Quantization and Riemannian-Symplectic Manifolds

Abstract

We develop a mathematically well-defined path integral formalism for general symplectic manifolds. We argue that in order to make a path integral quantization covariant under general coordinate transformations on the phase space and involve a genuine functional measure that is both finite and countably additive, the phase space manifold should be equipped with a Riemannian structure (metric). A suitable method to calculate the metric is also proposed.

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References in corpus (3)

• Coherent State Quantization of Constraint Systems
• Coordinate-Free Quantization of Second-Class Constraints
• Coordinate-free quantization of first-class constrained systems

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