Semianalytical Calculation of the O⁺⁺ Glueball Mass in Su(2) Gauge Theory

Citation

Kolawa, Adam (1986) Semianalytical Calculation of the O⁺⁺ Glueball Mass in Su(2) Gauge Theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z4HC-3T81. https://resolver.caltech.edu/CaltechETD:etd-12072004-144217

Abstract

An attempt is made to derive and to solve the Schrodinger equation in the low energy region (vacuum, first excitation etc.) of the lattice. The complete orthonormal basis in the physical Hilbert space is constructed by classifying independent solutions of the 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 Schrodinger equation is solved in the (truncated) loop basis.

The resulting physical picture for the Yang-Mills vacuum in the cross-over region is that of, still quite dilute, gas of fluctuating loops. The glueball in this formalism looks like a local inhomogeneity in the loop distribution. 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.

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