Defining the force between separated sources on a light front - art. no. 045001

The Newtonian character of gauge theories on a light front requires that th e longitudinal momentum P+, which plays the role of Newtonian mass, be cons erved. This requirement conflicts with the standard definition of the force between two sources in terms of the minimal energy of quantum gauge fields in the presence of a quark and anti-quark pinned to points separated by a distance R. We propose that, on a light front, the force be defined by mini mizing the energy of gauge fields in the presence of a quark and an anti-qu ark pinned to lines (1-branes) oriented in the longitudinal direction singl ed out by the light front and separated by a transverse distance R. Such so urces will have a limited 1+1 dimensional dynamics. We study this proposal for weak coupling gauge theories by showing how it leads to the Coulomb for ce law. For QCD we also show how asymptotic freedom emerges by evaluating t he S matrix through one loop for the scattering of a particle in the N-c re presentation of color SU(N-c) on a 1-brane by a particle in the (N) over ba r(c) representation of color on a parallel 1-brane separated from the first by a distance R much less than 1/Lambda(QCD). Potential applications to th e problem of confinement on a light front are discussed. [S0556-2821(99)026 14-4].