Wavelet representation of light-front quantum field theory

Abstract

A formally exact discrete multiresolution representation of quantum field theory on a light front is presented. The formulation uses an orthonormal basis of compactly supported wavelets to expand the fields restricted to a light front. The representation has a number of useful properties. First, light-front preserving Poincaré transformations can be computed by transforming the arguments of the basis functions. The discrete field operators, which are defined by integrating the product of the field and a basis function over the light front, represent localized degrees of freedom on the light-front hyperplane. These discrete fields are irreducible and the vacuum is formally trivial. The light-front Hamiltonian and all of the Poincaré generators are linear combinations of normal ordered products of the discrete field operators with analytically computable constant coefficients. The representation is discrete and has natural resolution and volume truncations like lattice formulations. Because it is formally exact, it is possible to systematically compute corrections for eliminated degrees of freedom.