Yang-Mills vacuum: An attempt at lattice loop calculus

• Published in: Nuclear physics. B 1987, Vol.291, p.594-628
• Main Authors: Furmanski, W., Kolawa, A.
• Format: Article
• Language: English
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/0550-3213(87)90487-1

An attempt is made to derive and to solve the Schrödinger equation in the low energy region (vacuum, first excitation, etc.) of the Yang-Mills theory on the lattice. The complete orthonormal basis in the physical Hilbert space is constructed by classifying independent solutions of Gauss' law. Loops of electric flux are chosen as elementary variables. The loop space hamiltonian is derived, an ansatz is made for the low energy wave functionals and the Schrödinger equation is solved in the (truncated) loop basis. The resulting physical picture for the Yang-Mills vacuum in the crossover region is that of a still quite dilute, gas of fluctuating loops. A definite candidate for the confining force emerges: the repulsive non-abelian loop-loop interaction (rather weak but persistent) generates an effective external field (“external pressure”) prohibiting unbounded loop size fluctuations. The negative sign (repulsion) is universal for all compact groups. Preliminary numerical results, so far mainly of an illustrative character, are presented.