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.

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 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

scholarly journals Corrections to Wigner–Eckart Relations by Spontaneous Symmetry Breaking

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1120
Author(s):  
Carlo Heissenberg ◽  
Franco Strocchi
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Irreducible Representations ◽  
Matrix Elements ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Goldstone Bosons ◽  
The Matrix ◽  
Symmetry Breaking Term ◽  
Breaking Term

The matrix elements of operators transforming as irreducible representations of an unbroken symmetry group G are governed by the well-known Wigner–Eckart relations. In the case of infinite-dimensional systems, with G spontaneously broken, we prove that the corrections to such relations are provided by symmetry breaking Ward identities, and simply reduce to a tadpole term involving Goldstone bosons. The analysis extends to the case in which an explicit symmetry breaking term is present in the Hamiltonian, with the tadpole term now involving pseudo Goldstone bosons. An explicit example is discussed, illustrating the two cases.

EFFECTIVE ACTION OF SIGMA MODEL ANOMALIES WITH EXTERNAL GAUGE FIELDS

1986 ◽  
Vol 01 (01) ◽  
pp. 23-27 ◽  
Author(s):  
YIE-LIANG WU ◽  
YAN-BO XIE ◽  
GUANG-ZHAO ZHOU
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Effective Action ◽  
Sigma Model ◽  
Original Model ◽  
Gauge Fields ◽  
Nonlinear Sigma Model ◽  
Consistency Conditions ◽  
Goldstone Bosons ◽  
External Gauge

The nonlinear sigma model describes Goldstone bosons originating from spontaneous symmetry breaking. A set of local counterterms is found to shift the anomaly of the nonlinear sigma model to that of the original model with fermions interacting with external gauge fields. The ‘t Hooft consistency conditions are matched automatically.

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