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

Abstract

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.

Spontaneous Symmetry Breaking in Systems Obeying the Dynamics of On–Off Intermittency and Presenting Bimodal Amplitude Distributions

“…As has recently been shown [7,24] and according to the 𝜑 theory, systems of finite size that undergo a second-order phase transition present a hysteresis zone between the…”

“…As has recently been shown [7,24] and according to the ϕ 4 theory, systems of finite size that undergo a second-order phase transition present a hysteresis zone between the pseudocritical point and the completion of the SSB, where the critical state continues to survive, also referred to as the "SSB-zone". Within this hysteresis zone, the single minimum of the Landau free energy, appearing at the value of the control parameter that corresponds to the symmetrical phase (pseudocritical point), is replaced by a degenerate set of minima.…”

Tachyon Behavior Due to Mass-State Transitions at Scattering Vertices

“…Introductions to alternative theories are presented in Refs. [15][16][17][18][19][20][21]. More recent examples of alternative theories are presented in Refs.…”

“…[22][23][24][25][26][27][28][29][30][31][32][33][34]. They cover a range of topics, including expansion of the universe [16], inflation [22][23][24]31,33], the cosmological constant [25,26], dark energy [29], spontaneous symmetry breaking [19,27], rolling tachyons [15,17], trapped ions [30], condensation in magnetic compactification [34], and the possibility of tachyonic neutrinos [28,32].…”