NonDiophantine arithmetic as the mathematical foundation for quantum field theory
Abstract
The problem of infinities in quantum field theory (QRT) is a long standing problem in physics.For solving this problem, different renormalization techniques have been suggested but the problem still persists. Here we suggest another approachto the elimination of infinities in QFT, which is based on nonDiophantine arithmetics  a novel mathematical area that already found useful applications in physics. To achieve this goal, new nonDiophantine arithmetics are constructed and their properties are studied. This allows using these arithmetics for computing integrals describing Feynman diagrams. Although in the conventional QFT these integrals diverge, their nonDiophantine counterparts are convergent and rigorously defined.
 Publication:

arXiv eprints
 Pub Date:
 December 2021
 arXiv:
 arXiv:2201.13207
 Bibcode:
 2022arXiv220113207B
 Keywords:

 Physics  General Physics;
 81T16
 EPrint:
 33 pages