Towards a Spectral Proof of the Mass Gap in QCD?

Details Towards a Spectral Proof of the Mass Gap in QCD? Towards a Spectral Proof of the Mass Gap in QCD?

2001-07-09

arxiv.org/abs/hep-th/0107069v4

Int.J.Mod.Phys. A17 (2002) 926-935

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, plain Tex. The revised version is totally new

Scientific paper

10.1142/S0217751X02010327

Yang--Mills theory in four dimensions is studied by using the Coulomb gauge. The Coulomb gauge Hamiltonian involves integration of matrix elements of an operator P built from the Laplacian and from a first-order differential operator. The operator P is studied from the point of view of spectral theory of pseudo-differential operators on compact Riemannian manifolds, both when self-adjointness holds and when it is not fulfilled. In both cases, well-defined matrix elements of P are evaluated as a first step towards the more difficult problems of quantized Yang--Mills theory.

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