2012/05/14 by Alexander Dynin, Dynin, Alexander
Physics and Astronomy · #Crystallography and Radiation Phenomena #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.1205.3187
A non-perturbative and mathematically rigorous quantum Yang-Mills theory on\n4-dimensional Minkowski spacetime is set up in the functional framework of a\ncomplex nuclear Kree-Gelfand triple. It involves a symbolic calculus of\noperators with variational derivatives and a new kind of infinite-dimensional\nellipticity. In the temporal gauge and Schwinger first order formalism,\nYang-Mills equations become a semilinear hyperbolic system for which the\ngeneral Cauchy problem is reduced to initial data with compact supports. For a\nsimple compact Yang-Mills gauge group and the anti-normal quantization of\nYang-Mills energy-mass functional of initial data in a box, the quantum\nenergy-mass spectrum is a sequence of non-negative eigenvalues converging to\ninfinity. In particular, it has a positive mass gap. Furthermore, the\nenergy-mass spectrum is self-similar (including the mass gap) in the inverse\nproportion to an infrared cutoff of the classical energy scale.\n