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

The Gaussian time-dependent variational equations are used to explored the physics of (phi(4))(3+1) field theory. We have investigated the s tatic solutions and discussed the conditions of renormalization. Using these results and stability analysis we show that there are two viabl e non-trivial versions of (phi(4))(3+1). In the continuum limit the ba re coupling constant can assume b-->0(+) and b-->0(-), which yield wel l-defined asymmetric and symmetric solutions, respectively. We have al so considered small oscillations in the broken phase and shown that th ey give one and two meson modes of the theory. The resulting equation has a closed solution leading to a ''zero mode'' and vanished scatteri ng amplitude in the limit of infinite cutoff. (C) 1998 Academic Press.