Abstract semiclassical analysis of the van Hove model
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916626439340032 |
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| author | Falconi, Marco Fratini, Lorenzo |
| author_facet | Falconi, Marco Fratini, Lorenzo |
| contents | In this paper we study the semiclassical limit $\hslash\to 0$ of a completely solvable model in quantum field theory: the van Hove model, describing a scalar field created and annihilated by an immovable source. Despite its simplicity, the van Hove model possesses many characterizing features of quantum fields, especially in the infrared region. In particular, the existence of non-Fock ground and equilibrium states in the presence of infrared singular sources makes a representation-independent algebraic approach of utmost importance. We make use of recent representation-independent techniques of infinite dimensional semiclassical analysis to establish the Bohr correspondence principle for the dynamics, equilibrium states, and long-time asymptotics in the van Hove model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20603 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Abstract semiclassical analysis of the van Hove model Falconi, Marco Fratini, Lorenzo Mathematical Physics Functional Analysis Operator Algebras Primary: 81T05. Secondary: 81Q20, 81S05, 46N50, 43A95 In this paper we study the semiclassical limit $\hslash\to 0$ of a completely solvable model in quantum field theory: the van Hove model, describing a scalar field created and annihilated by an immovable source. Despite its simplicity, the van Hove model possesses many characterizing features of quantum fields, especially in the infrared region. In particular, the existence of non-Fock ground and equilibrium states in the presence of infrared singular sources makes a representation-independent algebraic approach of utmost importance. We make use of recent representation-independent techniques of infinite dimensional semiclassical analysis to establish the Bohr correspondence principle for the dynamics, equilibrium states, and long-time asymptotics in the van Hove model. |
| title | Abstract semiclassical analysis of the van Hove model |
| topic | Mathematical Physics Functional Analysis Operator Algebras Primary: 81T05. Secondary: 81Q20, 81S05, 46N50, 43A95 |
| url | https://arxiv.org/abs/2407.20603 |