1205.3187 (Alexander Dynin)

Pseudovariational operators and Quantum Yang-Mills theory    [PDF]

Alexander Dynin

Second quantization of a complexified Gelfand nuclear triple is performed in the sesqui-holomorphic Kree-Gelfand nuclear triple. Continuous operators in the Kree-Gelfand triples are pseudovariational operators, subject to an infinite dimensional pseudodifferential calculus. Noether Yang-Mills energy functional of constrained initial data for the classical Yang-Mills equations is designated to be the anti-normal symbol of the non-negative selfadjoint Yang-Mills energy operator with variational derivatives. The spectrum of the operator is a sequence increasing to infinity at least in arithmetical progression. In particular, there is a gap at the bottom of the spectrum.

View original: http://arxiv.org/abs/1205.3187