SU(3) Yang-Mills Hamiltonian in the flux-tube gauge: Strong coupling expansion and glueball dynamics

Abstract: It is shown that the formulation of the SU(3) Yang-Mills quantum Hamiltonian in the "flux-tube gauge" $A_{a1}=0$ for all a=1,2,4,5,6,7 and $A_{a2}=0$ for all a=5,7 allows for a systematic and practical strong coupling expansion of the Hamiltonian in $\lambda\equiv g^{-2/3}$, equivalent to an expansion in the number of spatial derivatives. Introducing an infinite spatial lattice with box length a, the "free part" is the sum of Hamiltonians of Yang-Mills quantum mechanics of constant fields for each box, and the "interaction terms" contain higher and higher number of spatial derivatives connecting different boxes. The Faddeev-Popov operator, its determinant and inverse, are rather simple, but show a highly non-trivial periodic structure of six Gribov-horizons separating six Weyl-chambers. The energy eigensystem of the gauge reduced Hamiltonian of SU(3) Yang-Mills mechanics of spatially constant fields can be calculated in principle with arbitrary high precision using the orthonormal basis of all solutions of the corresponding harmonic oscillator problem, which turn out to be made of orthogonal polynomials of the 45 components of eight irreducible symmetric spatial tensors. First results for the low-energy glueball spectrum are obtained which substantially improve those by Weisz and Ziemann using the constrained approach. Thus, the gauge reduced approach using the flux-tube gauge proposed here, is expected to enable one to obtain valuable non-perturbative information about low-energy glueball dynamics, using perturbation theory in $\lambda$.