TY  - JOUR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Deformation quantization and boundary value problems
T2  - International journal of geometric methods in modern physics : differential geometery, algebraic geometery, global analysis & topology
N2  - 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.
KW  - Symplectic manifold
KW  - star product
KW  - trace
KW  - index
Y1  - 2016
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/45654
SN  - 0219-8878
SN  - 1793-6977
VL  - 13
SP  - 176
EP  - 195
PB  - World Scientific
CY  - Singapore
ER  -