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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2207.05667 |
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| _version_ | 1866909313737424896 |
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| author | Hawkins, Eli Minz, Christoph Rejzner, Kasia |
| author_facet | Hawkins, Eli Minz, Christoph Rejzner, Kasia |
| contents | Geometric quantization is a natural way to construct quantum models starting from classical data. In this work, we start from a symplectic vector space with an inner product and -- using techniques of geometric quantization -- construct the quantum algebra and equip it with a distinguished state. We compare our result with the construction due to Sorkin -- which starts from the same input data -- and show that our distinguished state coincides with the Sorkin-Johnson state. Sorkin's construction was originally applied to the free scalar field over a causal set (locally finite, partially ordered set). Our perspective suggests a natural generalization to less linear examples, such as an interacting field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_05667 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantization, dequantization, and distinguished states Hawkins, Eli Minz, Christoph Rejzner, Kasia Mathematical Physics Geometric quantization is a natural way to construct quantum models starting from classical data. In this work, we start from a symplectic vector space with an inner product and -- using techniques of geometric quantization -- construct the quantum algebra and equip it with a distinguished state. We compare our result with the construction due to Sorkin -- which starts from the same input data -- and show that our distinguished state coincides with the Sorkin-Johnson state. Sorkin's construction was originally applied to the free scalar field over a causal set (locally finite, partially ordered set). Our perspective suggests a natural generalization to less linear examples, such as an interacting field. |
| title | Quantization, dequantization, and distinguished states |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2207.05667 |