Physics, mathematics, and technology

2019 Issue №3

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1+1-Dimensional Yang — Mills Equations and Mass via Quasiclassi­cal Correction to Action



Two-dimensional Yang — Mills models in a pseudo-euclidean space are considered from a point of view of a class of nonlinear Klein — Gordon — Fock equations. It is shown that the Nahm reduction does not work, another, novel choice is proposed and investigated. A quasiclassical quantization of the models is based on Feynmann — Maslov path integral construction and its zeta function representation in terms of a Green function diagonal for an aux­iliary heat equation with an elliptic potential. The natural renormalization use a freedom in vacuum state choice as well as the choice of the norm of an evolu­tion operator eigenvectors. A nonzero mass appears as the quasiclassical cor­rection, that is expressed via hyperelliptic integral.


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