Observability and Mathematics:Quantum Yang-Mills Theory and Modelling

by: Boris Khots (Author)

Publisher: De Gruyter

Edition: 1st

Publication Date: 2024/7/1

Language: English

Print Length: 246 pages

ISBN-10: 3111397351

ISBN-13: 9783111397351

Book Description

Quantum Yang-Mills theory is now the foundation of most of elementary particle theory, and its predictions have been tested at many experimental laboratories, but its mathematical foundation is still unclear. The ”mass gap” property has been discovered by physicists from experiment, but it still has not been understood from a theoretical point of view. Proposed book describes author’s approach to solution of this problem on base of Mathematics with Observers (removing from arithmetic infinity idea, taking into account Observers dependent ascending chain of embedded sets of finite decimal fractions with arithmetic operations locally coinciding with standard operations, and getting new calculus, diff geometry, etc), including interpretations of vector fields and differential forms, generalization of Yang-Mills equations, proof of mass gap existing, consideration the theory of matrix Lie groups and algebras, and this point of view gives the possibilities to make new approach and establish the existence of the Yang-Mills theory and a mass gap, Grand unified theories and Standard model of particle physics.

About the Author

Quantum Yang-Mills theory is now the foundation of most of elementary particle theory, and its predictions have been tested at many experimental laboratories, but its mathematical foundation is still unclear. The ”mass gap” property has been discovered by physicists from experiment, but it still has not been understood from a theoretical point of view. Proposed book describes author’s approach to solution of this problem on base of Mathematics with Observers (removing from arithmetic infinity idea, taking into account Observers dependent ascending chain of embedded sets of finite decimal fractions with arithmetic operations locally coinciding with standard operations, and getting new calculus, diff geometry, etc), including interpretations of vector fields and differential forms, generalization of Yang-Mills equations, proof of mass gap existing, consideration the theory of matrix Lie groups and algebras, and this point of view gives the possibilities to make new approach and establish the existence of the Yang-Mills theory and a mass gap, Grand unified theories and Standard model of particle physics.

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