Spontaneous symmetry breaking in the phase space

In this brief, the spontaneous symmetry breaking (SSB) of the phi(4) theory in phase space, is studied. This phase space results from the appropriate system of Poincare maps, produced in both the Minkowski and the Euclidean time. The importance of discretization in the creation of phase space, is highlighted. A series of interesting, novel, unknown behaviors are reported for the first time; among them the most characteristic is the change in stability. In specific, the stable fixed points of the phi(4) potential appear as unstable ones, in phase space. Additionally, in the Euclidean-time phase space a unique instability in the position of the critical point, can be created. This instability is further proposed to host tachyonic field in Euclidean space.

Automated summary

This brief explores the spontaneous symmetry breaking of the phi(4) theory in phase space, using Poincare maps in both Minkowski and Euclidean time. It highlights the importance of discretization in creating phase space and reveals novel behaviors, with the most significant being a change in stability. The stable fixed points of the phi(4) potential are shown to become unstable in phase space, with unique instabilities and even the potential for hosting tachyonic fields in Euclidean space.