A mathematical approach to quantum field theory
Alexander Roi Stoyanovsky
TL;DR
This paper develops a mathematical framework for quantizing multidimensional variational principles and compares it with traditional quantum field theory, highlighting potential fundamental limitations in realizing QFT axioms.
Contribution
It introduces a new mathematical approach to quantum field theory quantization and discusses the possible non-existence of a complete axiomatic realization.
Findings
Mathematical quantization of multidimensional variational principles is developed.
Comparison with traditional quantum field theory constructions is provided.
Conjecture that a full mathematical realization of QFT axioms may not exist.
Abstract
We develop a mathematical theory of quantization of multidimensional variational principles, and compare it with traditional constructions of quantum field theory. We conjecture that mathematical realization of quantum field theory axioms, in general, does not exist.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra