Complexity in Tame Quantum Theories
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917656139923456 |
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| author | Grimm, Thomas W. Schlechter, Lorenz van Vliet, Mick |
| author_facet | Grimm, Thomas W. Schlechter, Lorenz van Vliet, Mick |
| contents | Inspired by the notion that physical systems can contain only a finite amount of information or complexity, we introduce a framework that allows for quantifying the amount of logical information needed to specify a function or set. We then apply this methodology to a variety of physical systems and derive the complexity of parameter-dependent physical observables and coupling functions appearing in effective Lagrangians. In order to implement these ideas, it is essential to consider physical theories that can be defined in an o-minimal structure. O-minimality, a concept from mathematical logic, encapsulates a tameness principle. It was recently argued that this property is inherent to many known quantum field theories and is linked to the UV completion of the theory. To assign a complexity to each statement in these theories one has to further constrain the allowed o-minimal structures. To exemplify this, we show that many physical systems can be formulated using Pfaffian o-minimal structures, which have a well-established notion of complexity. More generally, we propose adopting sharply o-minimal structures, recently introduced by Binyamini and Novikov, as an overarching framework to measure complexity in quantum theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_01484 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Complexity in Tame Quantum Theories Grimm, Thomas W. Schlechter, Lorenz van Vliet, Mick High Energy Physics - Theory High Energy Physics - Phenomenology Algebraic Geometry Logic Quantum Physics Inspired by the notion that physical systems can contain only a finite amount of information or complexity, we introduce a framework that allows for quantifying the amount of logical information needed to specify a function or set. We then apply this methodology to a variety of physical systems and derive the complexity of parameter-dependent physical observables and coupling functions appearing in effective Lagrangians. In order to implement these ideas, it is essential to consider physical theories that can be defined in an o-minimal structure. O-minimality, a concept from mathematical logic, encapsulates a tameness principle. It was recently argued that this property is inherent to many known quantum field theories and is linked to the UV completion of the theory. To assign a complexity to each statement in these theories one has to further constrain the allowed o-minimal structures. To exemplify this, we show that many physical systems can be formulated using Pfaffian o-minimal structures, which have a well-established notion of complexity. More generally, we propose adopting sharply o-minimal structures, recently introduced by Binyamini and Novikov, as an overarching framework to measure complexity in quantum theories. |
| title | Complexity in Tame Quantum Theories |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology Algebraic Geometry Logic Quantum Physics |
| url | https://arxiv.org/abs/2310.01484 |