Time-Dependent Variational Principle for $φ^4$ Field Theory: RPA Approximation and Renormalization (II)

Details Time-Dependent Variational Principle for $φ^4$ Field Theory: RPA Approximation and Renormalization (II) Time-Dependent Variational Principle for $φ^4$ Field Theory: RPA Approximation and Renormalization (II)

1998-05-11

arxiv.org/abs/hep-th/9805061v1

Annals Phys. 269 (1998) 55-76

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1006/aphy.1998.5838

The Gaussian-time-dependent variational equations are used to explored the physics of $(\phi^4)_{3+1}$ 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 $(\phi^4)_{3+1}$. 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.

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