论文标题
非毒液算术作为量子场理论的数学基础
Non-Diophantine arithmetic as the mathematical foundation for quantum field theory
论文作者
论文摘要
量子场理论（QRT）中无限态的问题是物理学的长期存在问题。为了解决此问题，已经提出了不同的重新归一化技术，但问题仍然存在。在这里，我们建议另一种消除QFT中无限态的方法，QFT基于非二噬算术算术 - 一种新型的数学领域，已经在物理学中找到了有用的应用。为了实现这一目标，构建了新的非毒液算术，并研究了它们的特性。这允许使用这些算术来计算描述Feynman图的积分。尽管在常规的QFT中，这些积分有分歧，但它们的非二噬剂对应物是收敛性和严格定义的。
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.
