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 in the late Universe and glimpses of the early Universe phase transitions à la baryogenesis

2021 ◽  
Author(s):  
M. Sami ◽  
Radouane Gannouji
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Particle Physics ◽  
Landau Theory ◽  
Bubble Nucleation ◽  
Beyond The Standard Model ◽  
Electroweak Phase Transition ◽  
Ginzburg Landau

Spontaneous symmetry breaking is the foundation of electroweak unification and serves as an integral part of the model building beyond the standard model of particle physics and it also finds interesting applications in the late Universe. We review development related to obtaining the late cosmic acceleration from spontaneous symmetry breaking in the Universe at large scales. This phenomenon is best understood through Ginzburg–Landau theory of phase transitions which we briefly describe. Hereafter, we present elements of spontaneous symmetry breaking in relativistic field theory. We then discuss the “symmetron” scenario-based upon symmetry breaking in the late Universe which is realized by using a specific form of conformal coupling. However, the model is faced with “NO GO” for late-time acceleration due to local gravity constraints. We argue that the problem can be circumvented by using the massless [Formula: see text] theory coupled to massive neutrino matter. As for the early Universe, spontaneous symmetry breaking finds its interesting applications in the study of electroweak phase transition. To this effect, we first discuss in detail the Ginzburg–Landau theory of first-order phase transitions and then apply it to electroweak phase transition including technical discussions on bubble nucleation and sphaleron transitions. We provide a pedagogical exposition of dynamics of electroweak phase transition and emphasize the need to go beyond the standard model of particle physics for addressing the baryogenesis problem. Review ends with a brief discussion on Affleck–Dine mechanism and spontaneous baryogenesis. Appendixes include technical details on essential ingredients of baryogenesis, sphaleron solution, one-loop finite temperature effective potential and dynamics of bubble nucleation.

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.

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.

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.

scholarly journals Gauge theory approach to branes and spontaneous symmetry breaking

2017 ◽  
Vol 29 (03) ◽  
pp. 1750009 ◽  
Author(s):  
A. A. Zheltukhin
Keyword(s):  
Gauge Theory ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Vector Fields ◽  
Theory Approach ◽  
Tensor Fields ◽  
Broken Symmetries ◽  
Goldstone Bosons ◽  
Dimensional Minkowski Space ◽  
Poincaré Symmetry

We discuss the gauge theory approach to consideration of the Nambu–Goldstone bosons as gauge and vector fields represented by the Cartan forms of spontaneously broken symmetries. The approach is generalized to describe the fundamental branes in terms of [Formula: see text]-dimensional worldvolume gauge and massless tensor fields consisting of the Nambu–Goldstone bosons associated with the spontaneously broken Poincaré symmetry of the [Formula: see text]-dimensional Minkowski space.

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

ENERGY GAP, MASS GAP, AND SPONTANEOUS SYMMETRY BREAKING

2010 ◽  
Vol 25 (22) ◽  
pp. 4141-4148 ◽  
Author(s):  
YOICHIRO NAMBU
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Particle Physics ◽  
Energy Gap ◽  
50Th Anniversary ◽  
Bcs Theory ◽  
Historical Overview ◽  
University Of Illinois ◽  
Mass Gap ◽  
The University

This article is based on a talk given at a Symposium at the University of Illinois on the occasion to commemorate the 50th anniversary of BCS — I gave a historical overview of how BCS theory has come to be transplanted to particle physics and has helped solve its problems.

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