Time-Dependent Variational Principle for ${\varphi }^4$ Field Theory: RPA Approximation and Renormalization (II)

Abstract

The Gaussian-time-dependent variational equations are used to explored the physics of $({\varphi }^4{)}_{3+1}$ 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 $({\varphi }^4{)}_{3+1}$. In the continuum limit the bare coupling constant can assume $b\to 0^{+}$ and $b\to 0^{-}$, 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.

29 pages, LaTex file, to appear in Annals of Physics

References in corpus (2)

• Gaussian Time-Dependent Variational Principle for Bosons I - Uniform Case
• Small oscillations of a chiral Gross-Neveu system

Cited by in corpus (7)

• Self-Consistent Random Phase Approximation - Application to the Hubbard Model for finite number of sites
• Entanglement Entropy and Variational Methods: Interacting Scalar Fields
• Stern-Volmer Modeling of Steady-State Forster Energy Transfer Between Dilute, Freely Diffusing Membrane-Bound Fluorophores
• Dynamical symmetry breaking and the Nambu-Goldstone theorem in the Gaussian wave functional approximation
• Generalized Random Phase Approximation and Gauge Theories
• Study of Hadrons Using the Gaussian Functional Method in the O(4) Linear $\sigma$ Model
• Elementary excitations of a Higgs-Yukawa system