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 |
|---|---|
| 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 |
