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.

Broken Symmetries

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Quantum Physics ◽  
Higgs Mechanism ◽  
Goldstone Theorem ◽  
Abelian Gauge ◽  
Massless Particles ◽  
Broken Symmetries ◽  
Gauge Symmetries ◽  
Non Linear

Exlicitly and spontaneously broken symmetries in classical and quantum physics. The linear and non-linear σ‎-model. The Goldstone theorem and the appearance of massless particles. The extension to Abelian and non-Abelian gauge symmetries and the Brout–Englert–Higgs mechanism.

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 60 YEARS OF BROKEN SYMMETRIES IN QUANTUM PHYSICS: FROM THE BOGOLIUBOV THEORY OF SUPERFLUIDITY TO THE STANDARD MODEL

2009 ◽  
Vol 24 (35n37) ◽  
pp. 2802-2802 ◽  
Author(s):  
DMITRY V. SHIRKOV
Keyword(s):  
Standard Model ◽  
Particle Physics ◽  
Quantum Physics ◽  
Higgs Mechanism ◽  
Cooper Pairs ◽  
Current Standard ◽  
Broken Symmetries ◽  
Bogoliubov Theory ◽  
The Standard Model

A retrospective historical overview of the phenomenon of spontaneous symmetry breaking (SSB) in quantum theory, the issue that has been implemented in particle physics in the form of the Higgs mechanism. The main items are: – The Bogoliubov's microscopical theory of superfluidity (1946); – The BCS-Bogoliubov theory of superconductivity (1957); – Superconductivity as a superfluidity of Cooper pairs (Bogoliubov - 1958); – Transfer of the SSB into the QFT models (early 60s); – The Higgs model triumph in the electro-weak theory (early 80s). The role of the Higgs mechanism and its status in the current Standard Model is also touched upon. Note from Publisher: This article contains the abstract only.

scholarly journals Vector Field with a Bare Mass and the Higgs Mechanism

1976 ◽  
Vol 56 (3) ◽  
pp. 972-980
Author(s):  
M. Konoue ◽  
N. Nakanishi
Keyword(s):  
Vector Field ◽  
Higgs Mechanism ◽  
Bare Mass

scholarly journals REMARKS ON A CHERN–SIMONS-LIKE COUPLING

2011 ◽  
Vol 26 (37) ◽  
pp. 2813-2821
Author(s):  
PATRICIO GAETE
Keyword(s):  
Gauge Theory ◽  
Vector Field ◽  
Static Potential ◽  
Gauge Invariant ◽  
Massive Vector ◽  
Hidden Sector ◽  
Dependent Variables ◽  
Qualitative Nature ◽  
Path Dependent ◽  
Chern Simons

We consider the static quantum potential for a gauge theory which includes a light massive vector field interacting with the familiar U (1) QED photon via a Chern–Simons-like coupling, by using the gauge-invariant, but path-dependent, variables formalism. An exactly screening phase is then obtained, which displays a marked departure of a qualitative nature from massive axionic electrodynamics. The above static potential profile is similar to that encountered in axionic electrodynamics consisting of a massless axion-like field, as well as to that encountered in the coupling between the familiar U (1) QED photon and a second massive gauge field living in the so-called U (1)h hidden-sector, inside a superconducting box.

scholarly journals ON THE QUANTUM CHROMODYNAMICS OF A MASSIVE VECTOR FIELD IN THE ADJOINT REPRESENTATION

2013 ◽  
Vol 28 (14) ◽  
pp. 1350054 ◽  
Author(s):  
ALFONSO R. ZERWEKH
Keyword(s):  
Vector Field ◽  
Quantum Chromodynamics ◽  
Extra Dimensions ◽  
Scalar Fields ◽  
Discrete Symmetry ◽  
Adjoint Representation ◽  
Coupling Constants ◽  
Gauge Symmetries ◽  
Gauge Fixing ◽  
Definition Of

In this paper, we explore the possibility of constructing the quantum chromodynamics of a massive color-octet vector field without introducing higher structures like extended gauge symmetries, extra dimensions or scalar fields. We show that gauge invariance is not enough to constraint the couplings. Nevertheless, the requirement of unitarity fixes the values of the coupling constants, which otherwise would be arbitrary. Additionally, it opens a new discrete symmetry which makes the coloron stable and avoid its resonant production at a collider. On the other hand, a judicious definition of the gauge fixing terms modifies the propagator of the massive field making it well-behaved in the ultraviolet limit. The relation between our model and the more general approach based on extended gauge symmetries is also discussed.

Symmetry

2021 ◽  
pp. 52-64
Author(s):  
Adrian P Sutton
Keyword(s):  
Physical Properties ◽  
Equations Of Motion ◽  
Topological Defects ◽  
Phase Changes ◽  
Broken Symmetry ◽  
Broken Symmetries ◽  
Higher Dimensional ◽  
Continuous Symmetries ◽  
Dimensional Crystal ◽  
Deep Sense

Symmetry arises not only in the invariance of an object to certain operations, but also in invariance of the equations governing motion of particles. Noether’s theorem connects continuous symmetries of equations of motion to conservation laws. The concept of broken symmetry arises in phase changes and topological defects, such as dislocations and disclinations. The principle of symmetry compensation reveals a deep sense in which symmetry is never destroyed – broken symmetries relate variants of an object displaying reduced symmetry. Symmetry plays a fundamental role in characterising the physical properties of crystals through Neumann’s principle. The concept of quasiperiodicity is introduced and it is shown how it is related to periodicity in a higher dimensional crystal.

scholarly journals Superluminal Sound and Ferromagnetic Transition in the Zeldovich Model

1974 ◽  
Vol 53 ◽  
pp. 169-182
Author(s):  
G. Kalman ◽  
S. T. Lai
Keyword(s):  
Phase Transition ◽  
Vector Field ◽  
Sound Propagation ◽  
Relativistic Effects ◽  
Fermi Gas ◽  
Ferromagnetic Phase ◽  
Ferromagnetic Transition ◽  
Correlation Effects ◽  
Massive Vector ◽  
Maximal Density

The implications of the Zeldovich model (baryons interacting through a massive vector field) for the problem of superluminal sound propagation and ferromagnetic transition are examined. In a classical baryon gas at high densities correlation effects lead to the pressure increasing faster than the energy, ultimately resulting in superluminal sound; crystallization phase transition appears however at comparable densities, thus competing with the onset of superluminal sound. For a high density fermi gas the domains of ferromagnetic transition are delineated, indicating a minimal and maximal density below and above which no ferromagnetic transition can be expected. The latter is further affected by relativistic effects requiring a different approach to the calculation of exchange energy and of the ferromagnetic phase.

scholarly journals Dark energy as a massive vector field

2007 ◽  
Vol 50 (2) ◽  
pp. 423-429 ◽  
Author(s):  
C.G. Böhmer ◽  
T. Harko
Keyword(s):  
Dark Energy ◽  
Vector Field ◽  
Massive Vector
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