Indispensability of residual gauge fields and extended hamiltonian formalism in light-front quantization of gauge fields

Abstract

We consider introducing residual gauge degrees of freedom into the conventional formulation of the light-front quantization of gauge field theories. For that purpose we construct the canonical formulation of axial gauge fields of the type nμ Aμ = 0 in auxiliary coordinates: xμ = (xτ,xσ,x1,x2), where xτ = x0 sin φ + x3 cos φ and xσ = x0 cos φ − x3 sin φ. We then show that, irrespective of the quantization surface, and irrespective of the gauge fixing condition, residual gauge fields are indispensable in implementing the Mandelstam-Leibbrandt prescription and in regularizing the infrared divergences which are inherent in the canonical quantization of space-like axial gauge fields. With the residual gauge fields in place, we find that the infrared divergences are regulated with the Mandelstam-Leibbrandt prescription in the light-front formulation obtained as the limit φ→π/4 of the n2 = 0 case. In addition we show that, because an explicit quantization surface dependence does not appear in the n2 = 0 case, the light-front temporal gauge limit φ→π/4−0 agrees with the light-front spatial gauge limit φ→π/4+0 and that the perturbative Hamiltonian in the light-front formulation consists of physical degrees of freedom integrated over the hyperplane xl+ = (x0+x3)/√2 = constant and residual degrees of freedom integrated over the hyperplane xl− = (x0 − x3)/√2 = constant.