Complexity in Tame Quantum Theories

• URL: http://arxiv.org/abs/2310.01484v2
• Date: Fri, 3 May 2024 13:41:13 GMT
• Title: Complexity in Tame Quantum Theories
• Authors: Thomas W. Grimm, Lorenz Schlechter, Mick van Vliet,
• Abstract summary: We introduce a framework that allows for quantifying the amount of logical information needed to specify a function or set. We derive the complexity of parameter-dependent physical observables and coupling functions appearing in effective Lagrangians.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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