On logical problems arising in atomic and particle physics

Abstract: In this talk, I will present certain ideas from quantum field theory that lead to mathematical problems typically addressed in mathematical logic literature. This will be an overview talk, accessible to a general logic audience, and it will have four main themes:

1) evidence that non computable functions arise in dynamics of elementary particles. I will discuss how this non computability can manifest itself in precision measurements and what this means for quantum computing.

2) rigorous definition of path integral. I will formulate the problem in the language of Banach space theory, and discuss relations to recent work on Banach homological algebra.

3) higher quantizations and higher functionals. I will define a hierarchy of symmetric functionals of low complexity but arbitrarily high in the constructive universe, and show the relevance of this construction to physical observables.

4) quantum randomness vs mathematical randomness. I will compare these two notions of randomness and discuss what is the interplay with the hierarchies of definable function spaces and the problem in 2) of defining integration over function spaces. I will touch upon the measurement problem and its interpretation from a mathematical perspective.

logicatomic physicsquantum physics

Audience: researchers in the topic

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Online logic seminar

Series comments: Description: Seminar on all areas of logic

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