Higgs fields as Yang-Mills fields and discrete symmetries

1991 ◽  
Vol 353 (3) ◽  
pp. 689-706 ◽  
Author(s):  
R. Coquereaux ◽  
G. Esposito-Farese ◽  
G. Vaillant
Keyword(s):  
Discrete Symmetries ◽  
Yang Mills ◽  
Higgs Fields

scholarly journals Lévy differential operators and Gauge invariant equations for Dirac and Higgs fields

2019 ◽  
Vol 22 (01) ◽  
pp. 1950001 ◽  
Author(s):  
Boris O. Volkov
Keyword(s):  
Differential Operators ◽  
Equations Of Motion ◽  
Parallel Transport ◽  
System Of Differential Equations ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Dirac Equations ◽  
Lévy Laplacian ◽  
Higgs Fields

We study the Lévy infinite-dimensional differential operators (differential operators defined by the analogy with the Lévy Laplacian) and their relationship to the Yang–Mills equations. We consider the parallel transport on the space of curves as an infinite-dimensional analogue of chiral fields and show that it is a solution to the system of differential equations if and only if the associated connection is a solution to the Yang–Mills equations. This system is an analogue of the equations of motion of chiral fields and contains the Lévy divergence. The systems of infinite-dimensional equations containing Lévy differential operators, that are equivalent to the Yang–Mills–Higgs equations and the Yang–Mills–Dirac equations (the equations of quantum chromodynamics), are obtained. The equivalence of two ways to define Lévy differential operators is shown.

Heat flow for Yang-Mills-Higgs fields, part I

2000 ◽  
Vol 21 (4) ◽  
pp. 453-472
Author(s):  
Fang Yi ◽  
Hong Minchun
Keyword(s):  
Heat Flow ◽  
Yang Mills ◽  
Higgs Fields

scholarly journals Anomalies in the space of coupling constants and their dynamical applications II

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Clay Cordova ◽  
Daniel Freed ◽  
Ho Tat Lam ◽  
Nathan Seiberg
Keyword(s):  
Phase Transitions ◽  
Time Reversal ◽  
Discrete Symmetries ◽  
Gauge Theories ◽  
Coupling Constants ◽  
Global Symmetry ◽  
Flavor Symmetry ◽  
Fundamental Representation ◽  
Yang Mills ◽  
Simply Connected

We extend our earlier work on anomalies in the space of coupling constants to four-dimensional gauge theories. Pure Yang-Mills theory (without matter) with a simple and simply connected gauge group has a mixed anomaly between its one-form global symmetry (associated with the center) and the periodicity of the \thetaθ-parameter. This anomaly is at the root of many recently discovered properties of these theories, including their phase transitions and interfaces. These new anomalies can be used to extend this understanding to systems without discrete symmetries (such as time-reversal). We also study SU(N)SU(N) and Sp(N)Sp(N) gauge theories with matter in the fundamental representation. Here we find a mixed anomaly between the flavor symmetry group and the \thetaθ-periodicity. Again, this anomaly unifies distinct recently-discovered phenomena in these theories and controls phase transitions and the dynamics on interfaces.

scholarly journals Higgs fields induced by Yang–Mills type Lagrangians on gauge-natural prolongations of principal bundles

2019 ◽  
Vol 16 (03) ◽  
pp. 1950049
Author(s):  
Marcella Palese ◽  
Ekkehart Winterroth
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Higgs Field ◽  
Field Theories ◽  
Conserved Quantities ◽  
Principal Bundles ◽  
Yang Mills ◽  
Covariant Gauge ◽  
Higgs Fields ◽  
Natural Bundle

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.

Towards a unified treatment of Yang-Mills and Higgs fields: A supersymmetric extension

1992 ◽  
Vol 46 (10) ◽  
pp. 4698-4703 ◽  
Author(s):  
B. S. Balakrishna ◽  
Feza Gürsey ◽  
Nguyen Ai Viet ◽  
Kameshwar C. Wali
Keyword(s):  
Supersymmetric Extension ◽  
Yang Mills ◽  
Higgs Fields

scholarly journals ALGEBRAIC CONNECTIONS ON PARALLEL UNIVERSES

1995 ◽  
Vol 10 (01) ◽  
pp. 89-98 ◽  
Author(s):  
R. COQUEREAUX ◽  
R. HÄUβLING ◽  
F. SCHECK
Keyword(s):  
Noncommutative Geometry ◽  
Associative Algebra ◽  
Differential Algebra ◽  
Yang Mills ◽  
Parallel Universes ◽  
Definition Of ◽  
Higgs Fields

For any manifold M we introduce a ℤ-graded differential algebra Ξ, which, in particular, is a bimodule over the associative algebra C(M⋃M). We then introduce the corresponding covariant differentials and show how this construction can be interpreted in terms of Yang-Mills and Higgs fields. This is a particular example of noncommutative geometry. It differs from the prescription of Connes in the following way: the definition of Ξ does not rely on a given Dirac-Yukawa operator acting on a space of spinors.

scholarly journals Convergence of Yang–Mills–Higgs fields

2015 ◽  
Vol 366 (1-2) ◽  
pp. 167-217 ◽  
Author(s):  
Chong Song
Keyword(s):  
Yang Mills ◽  
Higgs Fields
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