Time-Dependent Variational Principle forφ4Field Theory: RPA Approximation and Renormalization (II)

✍ Scribed by Arthur K. Kerman; Chi-Yong Lin

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 326 KB
• Volume: 269
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.1998.5838

✦ Synopsis

The Gaussian time-dependent variational equations are used to explored the physics of (, 4 ) 3+1 field theory. We have investigated the static solutions and discussed the conditions of renormalization. Using these results and stability analysis we show that there are two viable non-trivial versions of (, 4 ) 3+1 . In the continuum limit the bare coupling constant can assume b Ä 0 + and b Ä 0 & , which yield well-defined asymmetric and symmetric solutions, respectively. We have also considered small oscillations in the broken phase and shown that they give one and two meson modes of the theory. The resulting equation has a closed solution leading to a ``zero mode'' and vanished scattering amplitude in the limit of infinite cutoff.

1998 Academic Press

I. INTRODUCTION

In a recent paper [1] (hereafter referred to as I) we have obtained the RPA equations for , 4 field theory by linearizing the time-dependent variational equations. The method was implemented for the case of symmetric vacuum, (,) =0, which allows us to investigate two-meson physics. We have shown that it is a simple nonperturbative method to study scattering processes. Using this framework the problem of stability of vacuum can be explored from the RPA modes. In continuation of I we will consider here the stability of the theory for other critical points of the Gaussian parameter space [2]. In particular, we discuss the solutions and renormalization conditions for the asymmetric vacuum. In this case, the Article No. PH985838 55 0003-4916Â98 25.00