Spontaneous symmetry breaking: the Goldstone theorem and the Higgs phenomenon

1996 ◽  
pp. 40-48 ◽  
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Goldstone Theorem

scholarly journals Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories

2018 ◽  
Vol 98 (4) ◽  
Author(s):  
Jean Alexandre ◽  
John Ellis ◽  
Peter Millington ◽  
Dries Seynaeve
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Field Theories ◽  
Goldstone Theorem

scholarly journals The Quantum Yang-Baxter Conditions: The Fundamental Relations behind the Nambu-Goldstone Theorem

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 803 ◽  
Author(s):  
Ivan Arraut
Keyword(s):  
Dispersion Relation ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Goldstone Theorem ◽  
Goldstone Bosons

We demonstrate that when there is spontaneous symmetry breaking in any system, relativistic or non-relativistic, the dynamic of the Nambu-Goldstone bosons is governed by the Quantum Yang-Baxter equations. These equations describe the triangular dynamical relations between pairs of Nambu-Goldstone bosons and the degenerate vacuum. We then formulate a theorem and a corollary showing that these relations guarantee the appropriate dispersion relation and the appropriate counting for the Nambu-Goldstone bosons.

My Life as a Boson: The Story of "The Higgs"

2012 ◽  
Vol 01 (02) ◽  
pp. 50-51
Author(s):  
Peter Higgs
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Landau Theory ◽  
Scalar Fields ◽  
Bcs Theory ◽  
Goldstone Theorem ◽  
Ginzburg Landau ◽  
Goldstone Bosons ◽  
Massless Spin ◽  
The Subject

The story begins in 1960, when Nambu, inspired by the BCS theory of superconductivity, formulated chirally invariant relativistic models of interacting massless fermions in which spontaneous symmetry breaking generates fermionic masses (the analogue of the BCS gap). Around the same time Jeffrey Goldstone discussed spontaneous symmetry breaking in models containing elementary scalar fields (as in Ginzburg-Landau theory). I became interested in the problem of how to avoid a feature of both kinds of model, which seemed to preclude their relevance to the real world, namely the existence in the spectrum of massless spin-zero bosons (Goldstone bosons). By 1962 this feature of relativistic field theories had become the subject of the Goldstone theorem.

scholarly journals Spontaneous symmetry breaking and Nambu–Goldstone modes in open classical and quantum systems

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
Yoshimasa Hidaka ◽  
Yuki Minami
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Type A ◽  
Quantum Systems ◽  
Propagation Mode ◽  
Goldstone Mode ◽  
Type B ◽  
Goldstone Theorem ◽  
Diffusion Type ◽  
Goldstone Modes

Abstract We discuss spontaneous symmetry breaking of open classical and quantum systems. When a continuous symmetry is spontaneously broken in an open system, a gapless excitation mode appears corresponding to the Nambu–Goldstone mode. Unlike isolated systems, the gapless mode is not always a propagation mode, but it is a diffusion one. Using the Ward–Takahashi identity and the effective action formalism, we establish the Nambu–Goldstone theorem in open systems, and derive the low-energy coefficients that determine the dispersion relation of Nambu–Goldstone modes. Using these coefficients, we classify the Nambu–Goldstone modes into four types: type-A propagation, type-A diffusion, type-B propagation, and type-B diffusion modes.

scholarly journals The Nambu–Goldstone theorem in nonrelativistic systems

2017 ◽  
Vol 32 (21) ◽  
pp. 1750127 ◽  
Author(s):  
Ivan Arraut
Keyword(s):  
Dispersion Relation ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Necessary Conditions ◽  
Goldstone Theorem ◽  
Goldstone Bosons

In nonrelativistic systems, when there is spontaneous symmetry breaking, the number of Nambu–Goldstone bosons [Formula: see text] are not necessarily equal to the number of broken generators [Formula: see text]. Here we use the method of operators for analyzing the necessary conditions in order to obtain the correct dispersion relation for the Nambu–Goldstone bosons.

Spontaneous symmetry breaking of dislocation core in SrTiO3

2021 ◽  
pp. 100453
Author(s):  
Hetian Chen ◽  
Di Yi ◽  
Ben Xu ◽  
Jing Ma ◽  
Cewen Nan
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Dislocation Core

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

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1358
Author(s):  
Yiannis Contoyiannis ◽  
Michael P. Hanias ◽  
Pericles Papadopoulos ◽  
Stavros G. Stavrinides ◽  
Myron Kampitakis ◽  
...  
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Critical Point ◽  
Universality Class ◽  
Lattice Simulation ◽  
Ginzburg Landau ◽  
Spin Lattice ◽  
Nuclear Collisions ◽  
Ising Spin ◽  
Relativistic Nuclear Collisions

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.

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