Deformation quantization on the cotangent bundle of a Lie group
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866911890099142656 |
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| author | Domański, Ziemowit |
| author_facet | Domański, Ziemowit |
| contents | We develop a complete theory of non-formal deformation quantization on the cotangent bundle of a weakly exponential Lie group. An appropriate integral formula for the star-product is introduced together with a suitable space of functions on which the star-product is well defined. This space of functions becomes a Frechet algebra as well as a pre-C*-algebra. Basic properties of the star-product are proved and the extension of the star-product to a Hilbert algebra and an algebra of distributions is given. A C*-algebra of observables and a space of states are constructed. Moreover, an operator representation in position space is presented. Finally, examples of weakly exponential Lie groups are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1804_06950 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Deformation quantization on the cotangent bundle of a Lie group Domański, Ziemowit Mathematical Physics We develop a complete theory of non-formal deformation quantization on the cotangent bundle of a weakly exponential Lie group. An appropriate integral formula for the star-product is introduced together with a suitable space of functions on which the star-product is well defined. This space of functions becomes a Frechet algebra as well as a pre-C*-algebra. Basic properties of the star-product are proved and the extension of the star-product to a Hilbert algebra and an algebra of distributions is given. A C*-algebra of observables and a space of states are constructed. Moreover, an operator representation in position space is presented. Finally, examples of weakly exponential Lie groups are given. |
| title | Deformation quantization on the cotangent bundle of a Lie group |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/1804.06950 |