非丢番图算法作为量子场论的数学基础
Non-Diophantine arithmetic as the mathematical foundation for quantum field theory
摘要：
量子场论（QRT）中的无穷大问题是物理学中一个长期存在的问题，为了解决这个问题，人们提出了不同的重整化方法，但这个问题仍然存在.在这里，我们提出了另一种方法来消除QFT中的无穷大，这是基于非丢番图算术-一个新的数学领域，已经在物理学中找到了有用的应用。为了实现这一目标，构造了新的非丢番图算法，并研究了它们的性质。这允许使用这些算法来计算描述费曼图的积分。虽然在传统的QFT这些积分发散，他们的非丢番图对应收敛和严格定义。
英文摘要：
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 non-Diophantine arithmetics - a novel mathematical area that already found useful applications in physics. To achieve this goal, new non-Diophantine 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 non-Diophantine counterparts are convergent and rigorously defined.
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