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Vacuum Stability of the $\mathcal{PT}$-Symmetric $\left( -\phi^{4}\right) $ Scalar Field Theory by Shalaby, Abouzeid M. is a scholarly article available to read on EtoBox.

What is Vacuum Stability of the $\mathcal{PT}$-Symmetric $\left( -\phi^{4}\right) $ Scalar Field Theory about?

In this work, we study the vacuum stability of the classical unstable $\left( -\phi^{4}\right) $ scalar field potential. Regarding this, we obtained the effective potential, up to second order in the coupling, for the theory in $1+1$ and $2+1$ space-time dimensions. We found that the obtained effective potential is bounded from below, which proves the vacuum stability of the theory in space-time dimensions higher than the previously studied $0+1$ case. In our calculations, we used the canonical quantization regime in which one deals with operators rather than classical functions used in the path integral formulation. Therefore, the non-Hermiticity of the effective field theory is obvious. Moreover, the method we employ implements the canonical equal-time commutation relations and the Heisenberg picture for the operators. Thus, the metric operator is implemented in the calculations of the transition amplitudes. Accordingly, the method avoids the very complicated calculations needed in other methods for the metric operator. To test the accuracy of our results, we obtained the exponential behavior of the vacuum condensate for small coupling values, which has been obtained in the liter

Author

Shalaby, Abouzeid M.

Published

2009

Language

EN