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An Approach to Building Quantum Field Theory Based on Non-Diophantine Arithmetics

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Abstract

The problem of infinities in quantum field theory (QFT) is a longstanding problem in particle physics. To solve this problem, different renormalization techniques have been suggested but the problem persists. Here we suggest another approach to the elimination of infinities in QFT, which is based on non-Diophantine arithmetics – a novel mathematical area that already found useful applications in physics, psychology, and other areas. To achieve this goal, new non-Diophantine arithmetics are constructed and their properties are studied. In addition, non-Diophantine integration is developed in these arithmetics. These constructions allow using constructed non-Diophantine arithmetics for computing integrals associated with Feynman diagrams. Although in the conventional QFT such integrals diverge, their non-Diophantine counterparts are convergent and rigorously defined. As the result, QFT becomes consistent with quantum experiments.

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Authors and Affiliations

  1. UCLA, Los Angeles, CA, 90095, USA

    Mark Burgin

  2. Artwork Conversion Software Inc., Manhattan Beach, CA, 90266, USA

    Felix Lev

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  1. Mark Burgin
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  2. Felix Lev
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Correspondence to Mark Burgin.

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Burgin, M., Lev, F. An Approach to Building Quantum Field Theory Based on Non-Diophantine Arithmetics. Found Sci (2023). https://doi.org/10.1007/s10699-022-09881-x

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