Solitons and Instantons in the inverse {\phi}4 theory of critical phenomena. A proposal for the violation of causality of tachyonic field

TL;DR

This paper explores the existence and characteristics of solitons and instantons in inverse Ginzburg-Landau theory related to phase transitions, highlighting potential causality violations in tachyonic fields.

Contribution

It introduces a novel analysis of solitons and instantons in inverse G-L free energy, revealing their behavior in different space-time frameworks and implications for causality.

Findings

Solitons appear only in excited states during spontaneous symmetry breaking.

Static solitons persist in Minkowski space, while inverse G-L solitons become instantons in Euclidean space.

Causality violations in tachyonic fields may be addressed through soliton-instanton transitions.

Abstract

We investigate about the existence of static solitons solutions in the inverse G-L free energy in phase transitions of {\phi}4 theory. We calculate all the characteristics of these solitons , like localized structure, finite energy and mass . We show that solitons appears in spontaneous symmetry breaking (SSB) phenomenon only if the critical point is in excited state. When the time is introduced we shown that the static solitons of SSB remain as solitons in Minkowski space-time while the static solitons of inverse G-L free energy converted to instantons in Euclidean space. The violation of causality which appears in the tachyonic field could be faced passing from Minkowski solitons to Euclidean instantons.