Renormalizability of the functional schrödinger picture in Robertson-Walker space-time

Abstract

We study free and self-interacting scalar quantum field theories in a flat Robertson-Walker metric in the functional Schrödinger picture. We discuss Schrödinger picture quantization, relating it to conventional Heisenberg picture quantization. For the interacting theory, we introduce the time-dependent Gaussian approximation to study time evolution of pure and mixed states and we establish renormalizability of the approximation. We also study the question of computing a finite, renormalized energy-momentum tensor for both the free and the interacting theory in the Gaussian approximation. Using the adiabatic expansion, we show that the entire subtraction necessary to make the energy-momentum tensor finite in the free theory can be written in terms of covariantly conserved tensors. We further show that the same subtraction is sufficient to make the energy-momentum tensor finite in the Gaussian approximation for the interacting theory provided that the mass and coupling constants are renormalized.