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

Published on May 25, 2020in arXiv: Pattern Formation and Solitons
Y. Contoyiannis1
Estimated H-index: 1
Yiannis Contoyiannis19
Estimated H-index: 19
+ 2 AuthorsStavros G. Stavrinides10
Estimated H-index: 10
(International Hellenic University)
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.
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Spontaneous symmetry breaking usually occurs due to the tachyonic (spinodal) instability of a scalar field near the top of its effective potential at \ensuremath{\varphi}=0.Naively, one might expect the field \ensuremath{\varphi}to fall from the top of the effective potential and then experience a long stage of oscillations with amplitude O(v)near the minimum of the effective potential at \ensuremath{\varphi}=vuntil it gives its energy to particles produced during these oscillations....
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Introduction. Elementary Functions. Indefinite Integrals of Elementary Functions. Definite Integrals of Elementary Functions. Indefinite Integrals of Special Functions. Definite Integrals of Special Functions. Special Functions. Vector Field Theory. Algebraic Inequalities. Integral Inequalities. Matrices and Related Results. Determinants. Norms. Ordinary Differential Equations. Fourier, Laplace, and Mellin Transforms. Bibliographic References. Classified Supplementary References.
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