0 v 1 2 1 Ja n 19 99 Spherical gauge fields 1

We introduce the spherical field formalism for free gauge fields. We discuss the structure of the spherical Hamiltonian for both general covariant gauge and radial gauge and point out several new features not present in the scalar field case. We then use the evolution equations to compute gauge-field and field-strength correlators. 1 Overview Spherical field theory is a new non-perturbative method for studying quantum field theory. It was introduced in [1] to describe scalar boson interactions. The method utilizes the spherical partial wave expansion to reduce a general d-dimensional Euclidean functional integral into a set of coupled one-dimensional, radial systems. The coupled one-dimensional systems are then converted to differential equations which then can be solved using standard numerical methods. 4 The extension of the spherical field method to fermionic systems was described in [2]. In that analysis it was shown that the formalism avoids several difficulties which appear in the lattice treatment of fermions. These include fermion doubling, missing axial anomalies, and computational difficulties arising from internal fermion loops. This finding suggests that the spherical formalism could provide a useful method for studying gauge theories, especially those involving fermions. As a small but important initial step in this direction, we contribute the present work in which we introduce and discuss the spherical field method for free gauge 4 For free field theory these equations can be solved exactly, as we will demonstrate here for gauge fields.