Rotationally Symmetric Yang-Mills Gauge Theory and Generalized Uncertainty Principle

Abstract

Recently, it has been of considerably high interest to introduce the notion of minimal length in quantum mechanics and quantum field theories to get a proper description of quantum gravity. In this paper, we have attempted to unify the notion of minimal length with R×S^3 topological field theories which were introduced by Carmeli and Malin in 1985 [14]. We have collectively called this (R×S^3 )_H topological field theories where the “H” in the sub-script stands for Heisenberg’s notion of minimal length. A proper description for equations like Schrodinger’s equation, Klein-Gordon equation and QED, QCD Lagrangian on (R×S^3 )_H topology is derived. HIGHLIGHTS It has been of considerably high interest to incorporate existing theories with the notion of minimal length because it is thought to unify theories at large scale with the quantum world In this paper, we have done a similar unification by incorporating Rotaionally symmetric field theories with the notion of minimal length The derived equations work consistently under local and global gauge transformations