Spontaneously Broken Symmetries

2017 ◽  
Author(s):  
John Iliopoulos
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Ground State ◽  
Quantum Physics ◽  
Goldstone Boson ◽  
Massless Particle ◽  
Heisenberg Ferromagnet ◽  
Symmetric State ◽  
Broken Symmetries ◽  
Physical Particle

In this chapter we present the solution to the problem of mass. It is based on the phenomenon of spontaneous symmetry breaking (SSB). We first give the example of buckling, a typical example of spontaneous symmetry breaking in classical physics. We extract the main features of the phenomenon, namely the instability of the symmetric state and the degeneracy of the ground state. The associated concepts of the critical point and the order parameter are deduced. A more technical exposition is given in a separate section. Then we move to a quantum physics example, that of the Heisenberg ferromagnet. We formulate Goldstone’s theorem which associates a massless particle, the Goldstone boson, to the phenomenon of spontaneous symmetry breaking. In the last section we present the mechanism of Brout–Englert–Higgs (BEH). We show that spontaneous symmetry breaking in the presence of gauge interactions makes it possible for particles to become massive. The remnant of the mechanism is the appearance of a physical particle, the BEH boson, which we identify with the particle discovered at CERN.

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.

Spontaneously Broken Symmetries

2021 ◽  
pp. 287-303
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Phase Transitions ◽  
Vector Field ◽  
Quantum Physics ◽  
Goldstone Boson ◽  
Internal Symmetry ◽  
Higgs Mechanism ◽  
Broken Symmetry ◽  
Massive Vector ◽  
Broken Symmetries ◽  
Gauge Symmetries

The phenomenon of spontaneous symmetry breaking is a common feature of phase transitions in both classical and quantum physics. In a first part we study this phenomenon for the case of a global internal symmetry and give a simple proof of Goldstone’s theorem. We show that a massless excitation appears, corresponding to every generator of a spontaneously broken symmetry. In a second part we extend these ideas to the case of gauge symmetries and derive the Brout–Englert–Higgs mechanism. We show that the gauge boson associated with the spontaneously broken generator acquires a mass and the corresponding field, which would have been the Goldstone boson, decouples and disappears. Its degree of freedom is used to allow the transition from a massless to a massive vector field.

Chiral Symmetry

2019 ◽  
pp. 217-230
Author(s):  
Michael E. Peskin
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Chiral Symmetry ◽  
Goldstone Boson ◽  
Spontaneous Breaking ◽  
Quark Masses ◽  
Zero Mass ◽  
K Mesons ◽  
The Masses

This chapter introduces chiral symmetry, the extra symmetry that QCD acquires when the masses of quarks are set to zero. It introduces the concept of spontaneous symmetry breaking and explains the spontaneous breaking of chiral symmetry in QCD. It introduces the concept of a Goldstone boson, a particle that has zero mass as the result of spontaneous symmetry breaking, and explains how this concept explains properties of the pi and K mesons and allows us to determine the underlying values of the quark masses.

Spontaneous Symmetry Breaking

2018 ◽  
Vol 4 (2) ◽  
Author(s):  
Édouard Brézin
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Broken Symmetries ◽  
The Universe

Broken symmetries encompass a large number of different phenomena occurring at different scales. Édouard Brézin examines how symmetry has become central to understanding the organization of the universe.

scholarly journals Raising the SUSY-breaking scale in a Goldstone–Higgs model

2017 ◽  
Vol 32 (27) ◽  
pp. 1750143 ◽  
Author(s):  
Tommi Alanne ◽  
Heidi Rzehak ◽  
Francesco Sannino ◽  
Anders Eller Thomsen
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Supersymmetry Breaking ◽  
Goldstone Boson ◽  
Higgs Sector ◽  
Global Symmetry ◽  
Electroweak Sector ◽  
Chiral Superfield ◽  
Breaking Scale

We show that by combining the elementary Goldstone–Higgs scenario and supersymmetry it is possible to raise the scale of supersymmetry breaking to several TeVs by relating it to the spontaneous-symmetry-breaking one. This is achieved by first enhancing the global symmetries of the super-Higgs sector to SU(4) and then embedding the electroweak sector and the Standard Model (SM) fermions. We determine the conditions under which the model achieves a vacuum such that the resulting Higgs is a pseudo-Goldstone boson (pGB). The main results are: the supersymmetry-breaking scale is identified with the spontaneous-symmetry-breaking scale of SU(4) which is several TeVs above the radiatively induced electroweak scale; intriguingly the global symmetry of the Higgs sector predicts the existence of two super-Higgs multiplets with one mass eigenstate playing the role of the pseudo-Goldstone Higgs; the symmetry-breaking dynamics fixes [Formula: see text] and requires a supplementary singlet chiral superfield. We finally discuss the spectrum of the model that now features the superpartners of the SM fermions and gauge bosons in the multi-TeV range.

scholarly journals Abelian and non-abelian symmetries in infinite projected entangled pair states

2018 ◽  
Vol 5 (5) ◽  
Author(s):  
Claudius Hubig
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Ground State ◽  
Heisenberg Model ◽  
Computational Effort ◽  
Square Lattice ◽  
Two Dimensional ◽  
Computational Speed ◽  
Speed Up ◽  
Ground State Energies

We explore in detail the implementation of arbitrary abelian and non-abelian symmetries in the setting of infinite projected entangled pair states on the two-dimensional square lattice. We observe a large computational speed-up; easily allowing bond dimensions D=10D=10 in the square lattice Heisenberg model at computational effort comparable to calculations at D=6D=6 without symmetries. We also find that implementing an unbroken symmetry does not negatively affect the representative power of the state and leads to identical or improved ground-state energies. Finally, we point out how to use symmetry implementations to detect spontaneous symmetry breaking.

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