Deformation quantization and boundary value problems
- 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.
Author details: | Nikolai Nikolaevich TarkhanovORCiDGND |
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DOI: | https://doi.org/10.1142/S0219887816500079 |
ISSN: | 0219-8878 |
ISSN: | 1793-6977 |
Title of parent work (English): | International journal of geometric methods in modern physics : differential geometery, algebraic geometery, global analysis & topology |
Publisher: | World Scientific |
Place of publishing: | Singapore |
Publication type: | Article |
Language: | English |
Year of first publication: | 2016 |
Publication year: | 2016 |
Release date: | 2020/03/22 |
Tag: | Symplectic manifold; index; star product; trace |
Volume: | 13 |
Number of pages: | 30 |
First page: | 176 |
Last Page: | 195 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |