Gauge-invariant ground state for canonically quantized Yang-Mills theory

Details Gauge-invariant ground state for canonically quantized Yang-Mills theory Gauge-invariant ground state for canonically quantized Yang-Mills theory

2008-04-18

arxiv.org/abs/0804.3015v1

Physics

Mathematical Physics

20 pages, 0 figures. Submitted to Communications in Mathematical Physics

Scientific paper

We use Hamilton-Jacobi theory to construct a gauge-invariant zero-energy candidate ground state for canonically quantized Yang-Mills theory with a "nonlinear normal" factor ordering, generalizing an analogous ordering introduced by Moncrief and Ryan for problems with finitely many degrees of freedom. Invariance under spatial rotations and translations is immediate; boost invariance remains under investigation. The motivation is to find a model for constructing a candidate ground state in general relativity, canonically quantized a la the Ashtekar variables. We seek to avoid replicating some of the more troublesome features of the Kodama state, inherited from the Chern-Simons state.

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