Spontaneous symmetry breaking in the phase space

In this brief, the spontaneous symmetry breaking (SSB) of the \varphi^4theory 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...