Tachyons and Solitons in Spontaneous Symmetry Breaking in the Frame of Field Theory

• Main Authors: Yiannis Contoyiannis, Michael P. Hanias, Pericles Papadopoulos, Stavros G. Stavrinides, Myron Kampitakis, Stelios M. Potirakis, Georgios Balasis
• Format: Article
• Language: English
• Published: MDPI AG 2021-07-01
• Series: Symmetry
• Subjects: Ginzburg–Landau free energy; φ⁴ theory in phase transitions; tachyons; solitons; critical point of quantum chromo-dynamics (QCD)
• Online Access: https://www.mdpi.com/2073-8994/13/8/1358

This paper presents our study of the presence of the unstable critical point in spontaneous symmetry breaking (SSB) in the framework of Ginzburg–Landau (G-L) free energy. Through a 3D Ising spin lattice simulation, we found a zone of hysteresis where the unstable critical point continued to exist, despite the system having entered the broken symmetry phase. Within the hysteresis zone, the presence of the kink–antikink SSB solitons expands and, therefore, these can be observed. In scalar field theories, such as Higgs fields, the mass of this soliton inside the hysteresis zone could behave as a tachyon mass, namely as an imaginary quantity. Due to the fact that groups Ζ(2) and SU(2) belong to the same universality class, one expects that, in future experiments of ultra-relativistic nuclear collisions, in addition to the expected bosons condensations, structures of tachyon fields could appear.