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

We address some new issues concerning spontaneous symmetry breaking. We define classical Higgs fields for gauge-natural invariant Yang–Mills type Lagrangian field theories through the requirement of the existence of canonical covariant gauge-natural conserved quantities. As an illustrative example, we consider the ‘gluon Lagrangian’, i.e. a Yang–Mills Lagrangian on the [Formula: see text]-order gauge-natural bundle of [Formula: see text]-principal connections, and canonically define a ‘gluon’ classical Higgs field through the split reductive structure induced by the kernel of the associated gauge-natural Jacobi morphism.

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

Symmetry ◽

10.3390/sym11060803 ◽

2019 ◽

Vol 11 (6) ◽

pp. 803 ◽

Cited By ~ 7

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.

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

Asia Pacific Physics Newsletter ◽

10.1142/s2251158x12000264 ◽

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.

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

Progress of Theoretical and Experimental Physics ◽

10.1093/ptep/ptaa005 ◽

2020 ◽

Vol 2020 (3) ◽

Cited By ~ 1

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.

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HOW TO TREAT γ5

International Journal of Modern Physics A ◽

10.1142/s0217751x98001505 ◽

1998 ◽

Vol 13 (17) ◽

pp. 2991-3050 ◽

Cited By ~ 2

Author(s):

HUNG CHENG ◽

S. P. LI

Keyword(s):

Symmetry Breaking ◽

Vector Meson ◽

Spontaneous Symmetry Breaking ◽

Gauge Field ◽

Dimensional Regularization ◽

Gauge Field Theories ◽

Field Theories ◽

Chiral Fermion ◽

Gauge Invariant ◽

The Past

In the past two decades, Dyson's formalism of renormalization has been mostly superceded by dimensional regularization, particularly in the treatment of quantum gauge field theories with spontaneous symmetry breaking or those with chiral fermions. In this paper, we shall carry out explicitly Dyson's subtraction program, making it applicable to such field theories. In particular, we show with the example of the Abelian–Higgs theory how to handle amplitudes of chiral fermions. We show that these amplitudes which involve the γ5 matrix can be calculated in an unambiguous and gauge invariant way. This is done by establishing the subtraction conditions for the propagator of a chiral fermion as well as those for the VVV amplitude, when V denotes the vector meson. The renormalized constants are chosen to satisfy the Ward–Takahashi identities. As a demonstration, we calculate the next-lowest order correction of the anomaly in the Abelian–Higgs model and find that it vanishes.

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