scholarly journals Gauge gravitation theory: Gravity as a Higgs field

2016 ◽  
Vol 13 (06) ◽  
pp. 1650086 ◽  
Author(s):  
Gennadi Sardanashvily
Keyword(s):  
Gauge Theory ◽  
Symmetry Breaking ◽  
Riemannian Metrics ◽  
Higgs Field ◽  
Gravitation Theory ◽  
Gauge Fields ◽  
Linear Connections ◽  
Gauge Symmetries ◽  
Higgs Fields ◽  
Gauge Gravitation

Gravitation theory is formulated as gauge theory on natural bundles with spontaneous symmetry breaking, where gauge symmetries are general covariant transformations, gauge fields are general linear connections, and Higgs fields are pseudo-Riemannian metrics.

scholarly journals CLASSICAL GAUGE GRAVITATION THEORY

2011 ◽  
Vol 08 (08) ◽  
pp. 1869-1895 ◽  
Author(s):  
G. SARDANASHVILY
Keyword(s):  
Gravitational Field ◽  
Gauge Theory ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Higgs Field ◽  
Gravitation Theory ◽  
Gauge Symmetries ◽  
Gauge Gravitation ◽  
Natural Bundles

Classical gravitation theory is formulated as gauge theory on natural bundles where gauge symmetries are general covariant transformations and a gravitational field is a Higgs field responsible for their spontaneous symmetry breaking.

scholarly journals GEOMETRY OF CLASSICAL HIGGS FIELDS

2006 ◽  
Vol 03 (01) ◽  
pp. 139-148 ◽  
Author(s):  
G. SARDANASHVILY
Keyword(s):  
Gravitational Field ◽  
Gauge Theory ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Principal Bundle ◽  
Higgs Field ◽  
Global Section ◽  
Structure Group ◽  
Basic Facts ◽  
Higgs Fields

In gauge theory, Higgs fields are responsible for spontaneous symmetry breaking. In classical gauge theory on a principal bundle P, a symmetry breaking is defined as the reduction of a structure group of this principal bundle to a subgroup H of exact symmetries. This reduction takes place if and only if there exists a global section of the quotient bundle P/H. It is a classical Higgs field. A metric gravitational field exemplifies such a Higgs field. We summarize the basic facts on the reduction in principal bundles and geometry of Higgs fields. Our goal is the particular covariant differential in the presence of a Higgs field.

ZERO ENERGY GAUGE FIELDS AND THE PHASES OF A GAUGE THEORY

1990 ◽  
Vol 05 (14) ◽  
pp. 2783-2798 ◽  
Author(s):  
E.I. GUENDELMAN
Keyword(s):  
Gauge Theory ◽  
Gauge Fields ◽  
Zero Energy ◽  
Massless Particles ◽  
New Approach ◽  
Gauge Transformations ◽  
Definition Of ◽  
Higgs Fields ◽  
Invariant Gauge

A new approach to the definition of the phases of a Poincare invariant gauge theory is developed. It is based on the role of gauge transformations that change the asymptotic value of the gauge fields from zero to a constant. In the context of theories without Higgs fields, this symmetry can be spontaneously broken when the gauge fields are massless particles, explicitly broken when the gauge fields develop a mass. Finally, the vacuum can be invariant under this transformation, this last case can be achieved when the theory has a violent infrared behavior, which in some theories can be connected to a confinement mechanism.

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.

CONSTANT GAUGE FIELDS AND SYMMETRY BREAKING ON TORUS

1990 ◽  
Vol 05 (25) ◽  
pp. 2021-2029 ◽  
Author(s):  
CHOON-LIN HO
Keyword(s):  
Gauge Theory ◽  
Energy Density ◽  
Symmetry Breaking ◽  
Lower Energy ◽  
Field Configuration ◽  
Gauge Fields ◽  
Constant Field ◽  
Vacuum Gauge ◽  
Massless Fermion ◽  
Lower Energy Density

We examine symmetry breaking in an SU(2) gauge theory with a massless fermion defined on space-time manifold R1, d−3 × T2. Vacuum gauge field configuration is taken to have a constant field strength on the torus. Effective Potential in this background is evaluated and compared with that of pure gauge vacuum configuration. It is found that, in d ≡ 5, 7 (mod 8), vacuum with sufficiently large color magnetic flux on the torus could have lower energy density. This result applies to a U(1) theory as well. For SU(2) theory, the symmetry is broken to U(1).

scholarly journals SU(8) family unification with boson–fermion balance

2014 ◽  
Vol 29 (22) ◽  
pp. 1450130 ◽  
Author(s):  
Stephen L. Adler
Keyword(s):  
Perturbation Theory ◽  
Standard Model ◽  
Symmetry Breaking ◽  
Gauge Field ◽  
Gauge Coupling ◽  
Dynamical Symmetry ◽  
Gauge Fields ◽  
Yukawa Couplings ◽  
Gauge Symmetries ◽  
The Standard Model

We formulate an SU(8) family unification model motivated by requiring that the theory should incorporate the graviton, gravitinos, and the fermions and gauge fields of the standard model, with boson–fermion balance. Gauge field SU(8) anomalies cancel between the gravitinos and spin ½ fermions. The 56 of scalars breaks SU(8) to SU(3) family × SU(5) × U(1)/Z5, with the fermion representation content needed for "flipped" SU(5) with three families, and with residual scalars in the 10 and [Formula: see text] representations that break flipped SU(5) to the standard model. Dynamical symmetry breaking can account for the generation of 5 representation scalars needed to break the electroweak group. Yukawa couplings of the 56 scalars to the fermions are forbidden by chiral and gauge symmetries, so in the first stage of SU(8) breaking fermions remain massless. In the limit of vanishing gauge coupling, there are N = 1 and N = 8 supersymmetries relating the scalars to the fermions, which restrict the form of scalar self-couplings and should improve the convergence of perturbation theory, if not making the theory finite and "calculable." In an Appendix we give an analysis of symmetry breaking by a Higgs component, such as the (1, 1)(-15) of the SU(8) 56 under SU(8) ⊃ SU(3) × SU(5) × U(1), which has nonzero U(1) generator.

scholarly journals Dirac's Observables for the Higgs Model II: The Non-Abelian SU(2) Case

1997 ◽  
Vol 12 (26) ◽  
pp. 4797-4821 ◽  
Author(s):  
Luca Lusanna ◽  
Paolo Valtancoli
Keyword(s):  
Principal Bundle ◽  
A Priori ◽  
Canonical Basis ◽  
Higgs Field ◽  
Higgs Model ◽  
Gauge Fields ◽  
Coupling Constant ◽  
Non Local ◽  
Two Phases ◽  
Higgs Fields

We search a canonical basis of Dirac's observables for the classical non-Abelian Higgs model with fermions in the case of a trivial SU(2) principal bundle with a complex doublet of Higgs fields and with the fermions in a given representation of SU(2). Since each one of the three Gauss law first class constraints can be solved either in the corresponding longitudinal electric field or in the corresponding Higgs momentum, we get a priori eight disjoint phases of solutions of the model. The only two phases with SU(2) covariance are the SU(2) phase with massless SU(2) fields and the Higgs phase with massive SU(2) fields. The Dirac observables and the reduced physical (local) Hamiltonian and (non-local) Lagrangian of the Higgs phase are evaluated:the main result is the nonanalyticity in the SU(2) coupling constant, or equivalently in the sum of the residual Higgs field and of the mass of the SU(2) fields. Some comments on the function spaces needed for the gauge fields are made.

scholarly journals ON THE BV QUANTIZATION OF GAUGE GRAVITATION THEORY

2005 ◽  
Vol 02 (02) ◽  
pp. 203-226 ◽  
Author(s):  
D. BASHKIROV ◽  
G. SARDANASHVILY
Keyword(s):  
Gauge Theory ◽  
Gravitation Theory ◽  
Bv Quantization ◽  
Gauge Gravitation

Quantization of gravitation theory as gauge theory of general covariant transformations in the framework of Batalin–Vilkoviski (BV) formalism is considered. Its gauge-fixed Lagrangian is constructed.

scholarly journals SUPERMETRICS ON SUPERMANIFOLDS

2008 ◽  
Vol 05 (02) ◽  
pp. 271-286 ◽  
Author(s):  
G. SARDANASHVILY
Keyword(s):  
Gauge Theory ◽  
Lie Group ◽  
Closed Subgroup ◽  
Principal Bundle ◽  
Riemannian Metrics ◽  
Global Section ◽  
General Linear ◽  
Base Manifold ◽  
General Linear Supergroup ◽  
Higgs Fields

By virtue of the well-known theorem, a structure Lie group K of a principal bundle P → X is reducible to its closed subgroup H iff there exists a global section of the quotient bundle P/K → X. In gauge theory, such sections are treated as Higgs fields, exemplified by pseudo-Riemannian metrics on a base manifold X. Under some conditions, this theorem is extended to principal superbundles in the category of G-supermanifolds. Given a G-supermanifold M and a graded frame superbundle over M with a structure general linear supergroup, a reduction of this structure supergroup to an orthogonal-symplectic supersubgroup is associated to a supermetric on a G-supermanifold M.

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