K\"ahler polarisation and Wick Quantisation of Hamiltonian systems subject to second class constraints

TL;DR

This paper investigates conditions under which second-class constrained Hamiltonian systems can be endowed with an (almost) K"ahler structure and explores their deformation quantisation using Wick symbols for Dirac brackets.

Contribution

It establishes criteria for second-class constraint surfaces to be (almost) K"ahler manifolds and proposes a Wick-type deformation quantisation framework for these systems.

Findings

Conditions for second-class constraint surfaces to be (almost) K"ahler manifolds.

A sketch of deformation quantisation using Wick symbols for Dirac brackets.

Extension of geometric quantisation methods to constrained Hamiltonian systems.

Abstract

The necessary and sufficient conditions are established for the second-class constraint surface to be (an almost) K\"ahler manifold. The deformation quantisation for such systems is scetched resulting in the Wick-type symbols for the respective Dirac brackets.