Yang-Mills fields and Riemannian geometry

Abstract

It is possible to define new, gauge invariant variables in the Hilbert space of Yang-Mills theories which manifestly implement Gauss' law on physical states. These variables have furthermore a geometrical meaning, and allow one to uncover further constraints physical states must satisfy. For gauge group SU (2), the underlying geometry is Riemannian and based on the group GL(3). The formalism allows also for the inclusion of static color sources and the extension to gauge groups SU (N > 2), both of which are discussed here. CTP#2351UB-ECM-PF 94/21 08/94 *

Quantum mechanics of the vacuum state in two-dimensional QCD with adjoint fermions

“…Physical and unphysical degrees of freedom in non-abelian theories cannot be expected to simply factorize as in QED, and this complication does not depend on the number of space dimensions. Indeed the corresponding modifications of the electric field energy have been found in a variety of gauges [24,29,30,31]. In most cases, an explicit evaluation of the corresponding Jacobian is missing.…”

Gauge invariant geometric variables for Yang-Mills theory

“…In fact, this can be done in different ways [1]- [5]. In I., we have introduced such a transformation of variables, and here we will develop this formalism in more detail.…”

“…A new formulation of nonabelian gauge theory has recently been given [1] (hereafter referred to as I. ), which is founded on a geometrical basis and seeks to define a setting in which gauge symmetry is implemented exactly and manifestly, even under approximations of the dynamics.…”

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AbstractIn a previous publication [1], local gauge invariant geometric variables were introduced to describe the physical Hilbert space of Yang-Mills theory. In these variables, the electric energy involves the inverse of an operator which can generically have zero modes, and thus its calculation is subtle.

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Entropy bounds and Cardy–Verlinde formula in Yang–Mills theory

“…In the similar way in ref. [5], 4 dimensional Yang-Mills theory is presented in the Hamiltonian formulation in terms of 3 dimensional gravity 3 . The parametrization of the gauge field used in the paper corresponds to the expression of the spin connection by the dreibein fields.…”