Deformation quantisation and boundary value problems

Autoren: Nikolai Tarkhanov (2016)

We describe a natural construction of deformation quantization on a compact symplectic manifold with boundary. On the algebra of quantum observables a trace functional is defined which as usual annihilates the commutators. This gives rise to an index as the trace of the unity element. We formulate the index theorem as a conjecture and examine it by the classical harmonic oscillator.

Int. J. Geom. Methods Mod. Phys.

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