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The problem of infinities in quantum field theory (QRT) is a long standingproblem in physics.For solving this problem, different renormalizationtechniques have been suggested but the problem still persists. Here we suggestanother approachto the elimination of infinities in QFT, which is based onnon-Diophantine arithmetics - a novel mathematical area that already founduseful applications in physics. To achieve this goal, new non-Diophantinearithmetics are constructed and their properties are studied. This allows usingthese arithmetics for computing integrals describing Feynman diagrams. Althoughin the conventional QFT these integrals diverge, their non-Diophantinecounterparts are convergent and rigorously defined.

Non-Diophantine arithmetic as the mathematical foundation for quantum field theory