Spontaneous symmetry breaking in the phase space

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