Time-Dependent Variational Principle for φ4 Field Theory: 1. RPA Approximation and Renormalization

✍ Scribed by A.K. Kerman; C.Y. Lin

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 819 KB
• Volume: 241
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.1995.1060

✦ Synopsis

We investigate the time-dependent variational equations in (\phi^{4}) field theory. We show that the standard method for renormalization applies to these time-dependent equations. The crucial point is to use the hamiltonian nature of the variational principle. In particular we have considered small oscillations about equilibrium and shown that these give the two meson modes of the theory. The two meson equation has a closed solution leading to a single bound state for attractive renormalized coupling and a complete form for the scattering amplitude in the continuum. This form is easily adapted to the usual running coupling constant in the two meson energy. We also find that the massless solution is the lowest minimum for a range of renormalized coupling constant and that this minimum is not stable, implying that the actual lowest solution is not homogeneous. We have examined our equations for so called runaway solution where one of the physical parameters goes to infinity. Using the "potential" part of our variational hamiltonian we are able to show that conservation of energy prohibits any unphysical runaway. 1995 Academic Press, Inc.