Observability and Mathematics: Quantum Yang-Mills Theory and Modelling

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.

Boris Khots is a graduate of Lomonosov State University in Moscow, Russia. From 1996 to 2015, Dr. Khots worked at the Compressor Controls Corporation (CCC) in Des Moines, Iowa, USA. During his time at CCC, he held various positions such as Application Engineer, Senior Application Engineer, and Applications Engineering Leader. Dr. Khots’ research focused on control systems analysis and mathematical modeling, control algorithms, and control system implementation. Currently, Dr. Khots is self-employed as an independent researcher. He has over 150 scientific publications listed, with a main research focus on mathematics (mathematics with observers, Lie groups and algebras) and its application to physics.