Variational calculations with improved energy functionals in gauge theories

Abstract

For a SU(N) Yang-Mills theory, we present variational calculations using gaussian wave functionals combined with an approximate projection on gauge invariant states. The projection amounts to correcting the energy of the gaussian states by substracting the spurious energy associated with gauge rotations. Based on this improved energy functional, we perform variational calculations of the interaction energy in the presence of external electric and magnetic fields. We verify that the ultraviolet behaviour of our approximation scheme is consistent, as it should, with that expected from perturbation theory. In particular, we recover in this variational framework the standard one-loop beta function, with a transparent interpretation of the screening and anti-screening contributions.

40 pages, no figures

References in corpus (4)

• A variational approach to the QCD wavefunctional: Calculation of the QCD beta-function
• Ground State in Gluodynamics and Quark Confinement
• Equivalence of the Beta-function of the Variational Approach to that of QCD
• Interquark Potential in Schrodinger Representation

Cited by in corpus (5)

• Variational solution of the Yang-Mills Schrödinger equation in Coulomb gauge
• The Yang-Mills Vacuum in Coulomb Gauge in D=2+1 Dimensions
• Generalized Random Phase Approximation and Gauge Theories
• Gauge-invariant and infrared-improved variational analysis of the Yang-Mills vacuum wave functional
• Kamlah Expansion and Gauge Theories