Non-relativistic particle in a free random gauge background Original Research Article

The problem of a non-relativistic particle with an internal color degree of freedom, with and without spin, moving in a constant free random gauge background is discussed. Freeness is a concept developed recently in the mathematical literature connected with non-commuting random variables. In the context of large-N hermitian matrices, it means that the the multi-matrix model considered contains no bias with respect to the relative orientations of the matrices. In such a gauge background, one can solve analytically for the spectrum of a colored particle or, equivalently, the exact one-particle Greenʹs function. In three dimensions, near zero momentum, the energy distribution for the spinless particle displays a gap, while the energy distribution for the particle with spin does not.