Coherent manifolds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916651368185856 |
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| author | Neumaier, Arnold Bachler, Phillip Josef Farashahi, Arash Ghaani |
| author_facet | Neumaier, Arnold Bachler, Phillip Josef Farashahi, Arash Ghaani |
| contents | This paper defines coherent manifolds and discusses their properties and their application in quantum mechanics. Every coherent manifold with a large group of symmetries gives rise to a Hilbert space, the completed quantum space of $Z$, which contains a distinguished family of coherent states labeled by the points of the manifold.
The second quantization map in quantum field theory is generalized to quantization operators on arbitrary coherent manifolds. It is shown how the Schrödinger equation on any such completed quantum space can be solved in terms of computations only involving the coherent product. In particular, this applies to a description of Bosonic Fock spaces as completed quantum spaces of a class of coherent manifolds called Klauder spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09827 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coherent manifolds Neumaier, Arnold Bachler, Phillip Josef Farashahi, Arash Ghaani Mathematical Physics Differential Geometry Quantum Physics 81S10 (primary), 81R15, 47B32, 46C50, 46E22 This paper defines coherent manifolds and discusses their properties and their application in quantum mechanics. Every coherent manifold with a large group of symmetries gives rise to a Hilbert space, the completed quantum space of $Z$, which contains a distinguished family of coherent states labeled by the points of the manifold. The second quantization map in quantum field theory is generalized to quantization operators on arbitrary coherent manifolds. It is shown how the Schrödinger equation on any such completed quantum space can be solved in terms of computations only involving the coherent product. In particular, this applies to a description of Bosonic Fock spaces as completed quantum spaces of a class of coherent manifolds called Klauder spaces. |
| title | Coherent manifolds |
| topic | Mathematical Physics Differential Geometry Quantum Physics 81S10 (primary), 81R15, 47B32, 46C50, 46E22 |
| url | https://arxiv.org/abs/2503.09827 |