TIME-DEPENDENT VARIATIONAL PRINCIPLE FOR PHI(4) FIELD-THEORY .1. RPA APPROXIMATION AND RENORMALIZATION

We investigate the time-dependent variational equations in phi(4) fiel d theory. We show that the standard method for renormalization applies to these time-dependent equations. The crucial point is to use the ha miltonian nature of the variational principle. In particular we have c onsidered small oscillations about equilibrium and shown that these gi ve the two meson modes of the theory. The two meson equation has a clo sed solution leading to a single bound state for attractive renormaliz ed coupling and a complete form for the scattering amplitude in the co ntinuum. This form is easily adapted to the usual running coupling con stant in the two meson energy. We also find that the massless solution is the lowest minimum for a range of renormalized coupling constant a nd that this minimum is not stable, implying: that the actual lowest s olution is not homogeneous. We have examined our equations for so call ed runaway solution where one of the physical parameters goes to infin ity. Using the ''potential'' part of our variational hamiltonian we ar e able to show that conservation of energy prohibits any unphysical ru naway. (C) 1995 Academic Press, Inc.