Deformation quantisation and boundary value problems

We describe a natural construction of deformation quantisation 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.

Metadaten
Author details:	Boris Fedosov, Nikolai Nikolaevich Tarkhanov ORCiD GND
URN:	urn:nbn:de:kobv:517-opus4-77150
ISSN:	2193-6943
Publication series (Volume number):	Preprints des Instituts für Mathematik der Universität Potsdam (4 (2015) 5)
Publisher:	Universitätsverlag Potsdam
Place of publishing:	Potsdam
Publication type:	Preprint
Language:	English
Year of first publication:	2015
Publication year:	2015
Publishing institution:	Universität Potsdam
Publishing institution:	Universitätsverlag Potsdam
Release date:	2015/05/26
Tag:	index; star product; symplectic manifold; trace
Volume:	4
Issue:	5
Number of pages:	27
Organizational units:	Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:	5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC classification:	35-XX PARTIAL DIFFERENTIAL EQUATIONS
	53-XX DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx)
Collection(s):	Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2015
Publishing method:	Universitätsverlag Potsdam
License (German):	Keine öffentliche Lizenz: Unter Urheberrechtsschutz