scholarly journals Gauge-field-induced torsion and cosmic inflation

2021 ◽  
Vol 36 (21) ◽  
pp. 2150161
Author(s):  
Ammar Kasem ◽  
Shaaban Khalil
Keyword(s):  
General Relativity ◽  
Gauge Field ◽  
Natural Extension ◽  
Gauge Fields ◽  
Field Equations ◽  
Abelian Gauge ◽  
Cosmic Inflation ◽  
Coupling Procedure ◽  
Cartan Theory ◽  
Dynamical Field

In this paper, inflation in the framework of Einstein–Cartan theory is revisited. Einstein–Cartan theory is a natural extension of the General Relativity with nonvanishing torsion. The connection on Riemann–Cartan space–time is only compatible with the cosmological principal for a particular form of torsion. We also show this form to be compatible with gauge invariance principle for non-Abelian and Abelian gauge fields under a certain deviced coupling procedure. We adopt an Abelian gauge field in the form of “cosmic triad”. The dynamical field equations are obtained and shown to sustain cosmic inflation with a large number of e-folds. We emphasize that at the end of inflation, torsion vanishes and the theory of Einstein–Cartan reduces to the General Relativity with the usual FRW geometry.

scholarly journals PARTICLE SPECTRUM OF NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (14) ◽  
pp. 1137-1161 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Field ◽  
Free Field ◽  
Gauge Fields ◽  
Particle Spectrum ◽  
Field Equations ◽  
Abelian Gauge ◽  
Dimensional Spacetime ◽  
Higher Dimensional ◽  
Extended Field ◽  
Rank 2

We review the non-Abelian tensor gauge field theory and analyze its free field equations for lower rank gauge fields when the interaction coupling constant tends to zero. The free field equations are written in terms of the first-order derivatives of extended field strength tensors similar to the electrodynamics and non-Abelian gauge theories. We determine the particle content of the free field equations and count the propagating modes which they describe. In four-dimensional spacetime the rank-2 gauge field describes propagating modes of helicity two and zero. We show that the rank-3 gauge field describes propagating modes of helicity-three and a doublet of helicity-one gauge bosons. Only four-dimensional spacetime is physically acceptable, because in five- and higher-dimensional spacetime the equation has solutions with negative norm states. We discuss the structure of the particle spectrum for higher rank gauge fields.

scholarly journals Synthesis and observation of non-Abelian gauge fields in real space

Science ◽  
2019 ◽  
Vol 365 (6457) ◽  
pp. 1021-1025 ◽  
Author(s):  
Yi Yang ◽  
Chao Peng ◽  
Di Zhu ◽  
Hrvoje Buljan ◽  
John D. Joannopoulos ◽  
...  
Keyword(s):  
Gauge Field ◽  
Building Blocks ◽  
Real Space ◽  
Gauge Fields ◽  
Final States ◽  
Abelian Gauge ◽  
Classical Waves ◽  
Break Time ◽  
Bohm Effect ◽  
Aharonov Bohm

Particles placed inside an Abelian (commutative) gauge field can acquire different phases when traveling along the same path in opposite directions, as is evident from the Aharonov-Bohm effect. Such behaviors can get significantly enriched for a non-Abelian gauge field, where even the ordering of different paths cannot be switched. So far, real-space realizations of gauge fields have been limited to Abelian ones. We report an experimental synthesis of non-Abelian gauge fields in real space and the observation of the non-Abelian Aharonov-Bohm effect with classical waves and classical fluxes. On the basis of optical mode degeneracy, we break time-reversal symmetry in different manners, via temporal modulation and the Faraday effect, to synthesize tunable non-Abelian gauge fields. The Sagnac interference of two final states, obtained by reversely ordered path integrals, demonstrates the noncommutativity of the gauge fields. Our work introduces real-space building blocks for non-Abelian gauge fields, relevant for classical and quantum exotic topological phenomena.

scholarly journals On the Mathematics of Coframe Formalism and Einstein–Cartan Theory—A Brief Review

Universe ◽  
2019 ◽  
Vol 5 (10) ◽  
pp. 206 ◽  
Author(s):  
Manuel Tecchiolli
Keyword(s):  
Conservation Laws ◽  
Gauge Fields ◽  
Field Equations ◽  
Principal Bundles ◽  
Bianchi Identities ◽  
Cartan Theory

This article is a review of what could be considered the basic mathematics of Einstein–Cartan theory. We discuss the formalism of principal bundles, principal connections, curvature forms, gauge fields, torsion form, and Bianchi identities, and eventually, we will end up with Einstein–Cartan–Sciama–Kibble field equations and conservation laws in their implicit formulation.

scholarly journals MAXWELL SYMMETRIES AND SOME APPLICATIONS

2013 ◽  
Vol 23 ◽  
pp. 350-356 ◽  
Author(s):  
JOSÉ A. DE AZCÁRRAGA ◽  
KIYOSHI KAMIMURA ◽  
JERZY LUKIERSKI
Keyword(s):  
Gauge Theory ◽  
Gravity Field ◽  
Scalar Fields ◽  
Cosmological Term ◽  
Gauge Fields ◽  
Spin Connection ◽  
Field Equations ◽  
Geometric Framework ◽  
Abelian Gauge ◽  
Poincaré Algebra

The Maxwell algebra is the result of enlarging the Poincaré algebra by six additional tensorial Abelian generators that make the fourmomenta non-commutative. We present a local gauge theory based on the Maxwell algebra with vierbein, spin connection and six additional geometric Abelian gauge fields. We apply this geometric framework to the construction of Maxwell gravity, which is described by the Einstein action plus a generalized cosmological term. We mention a Friedman-Robertson-Walker cosmological approximation to the Maxwell gravity field equations, with two scalar fields obtained from the additional gauge fields. Finally, we outline further developments of the Maxwell symmetries framework.

scholarly journals Visible and hidden sectors in a model with Maxwell and Chern–Simons gauge dynamics

2016 ◽  
Vol 31 (34) ◽  
pp. 1650178 ◽  
Author(s):  
Edwin Ireson ◽  
Fidel A. Schaposnik ◽  
Gianni Tallarita
Keyword(s):  
Gauge Fields ◽  
Field Equations ◽  
Supersymmetric Extension ◽  
Abelian Gauge ◽  
Supersymmetric Version ◽  
Vortex Solutions ◽  
Set Up ◽  
Higgs Portal ◽  
Chern Simons ◽  
Two Sectors

We study a [Formula: see text] gauge theory discussing its vortex solutions and supersymmetric extension. In our set-up, the dynamics of one of two Abelian gauge fields is governed by a Maxwell term, the other by a Chern–Simons term. The two sectors interact via a BF gauge field mixing and a Higgs portal term that connects the two complex scalars. We also consider the supersymmetric version of this system which allows to find for the bosonic sector BPS equations in which an additional real scalar field enters into play. We study numerically the field equations finding vortex solutions with both magnetic flux and electric charge.

CHIRAL SPIN LIQUID STATES IN 3-SPACE DIMENSIONS AND TOPOLOGICAL ASPECTS OF MONOPOLE SUPERCONDUCTIVITY

1993 ◽  
Vol 07 (13n14) ◽  
pp. 913-919
Author(s):  
B. BASU ◽  
P. BANDYOPADHYAY
Keyword(s):  
Magnetic Flux ◽  
Gauge Field ◽  
Spin System ◽  
Berry Phase ◽  
Gauge Fields ◽  
Spin Liquid ◽  
Abelian Gauge ◽  
Heisenberg Spin ◽  
Pair Condensation ◽  
Liquid States

We have studied here the topological aspects of monopole superconductivity in 3+1 dimensions. It is pointed out that Heisenberg spin system may be associated with non-Abelian gauge fields. When the spin and charge become separated, spinons and holons emerge and holons interacting with such a gauge field associate a magnetic flux giving rise to nonzero Berry phase and causes the existence of chiral spin liquid. This also suggests that these holons are much heavier than their free counterpart and the pair of such holons forms a bosonic state respecting rotational invariance. Superconductivity arises out of this pair condensation.

scholarly journals Covariant-differential formulation of Lagrangian field theory

2018 ◽  
Vol 15 (08) ◽  
pp. 1850133
Author(s):  
Daniel Canarutto
Keyword(s):  
Field Theory ◽  
Gravitational Field ◽  
Gauge Fields ◽  
Field Equations ◽  
Jet Bundle ◽  
Abelian Gauge ◽  
Differential Formulation ◽  
Natural Vector ◽  
Lagrangian Field Theory ◽  
Vector Valued

Building on the Utiyama principle we formulate an approach to Lagrangian field theory in which exterior covariant differentials of vector-valued forms replace partial derivatives, in the sense that they take up the role played by the latter in the usual jet bundle formulation. Actually a natural Lagrangian can be written as a density on a suitable “covariant prolongation bundle”; the related momenta turn out to be natural vector-valued forms, and the field equations can be expressed in terms of covariant exterior differentials of the momenta. Currents and energy-tensors naturally also fit into this formalism. The examples of bosonic fields and spin one-half fields, interacting with non-Abelian gauge fields, are worked out. The “metric-affine” description of the gravitational field is naturally included, too.

scholarly journals ABOUT SOME EXACT SOLUTIONS FOR 2 + 1 GRAVITY COUPLED TO GAUGE FIELDS

1992 ◽  
Vol 07 (25) ◽  
pp. 2341-2350 ◽  
Author(s):  
IAN I. KOGAN
Keyword(s):  
Black Holes ◽  
Exact Solutions ◽  
Gauge Field ◽  
Three Dimensional ◽  
Einstein Gravity ◽  
Gauge Fields ◽  
Abelian Gauge ◽  
Planck Mass ◽  
Static Solutions

Some exact static solutions for Einstein gravity in 2 + 1 dimensions coupled to Abelian gauge field are discussed, where the invariant interval is of the form: ds2 = N2 (r) dt2 − dr2 − C2 (r) dθ2. Some of these solutions are three-dimensional analogs of the Schwarzschild black holes. The metrics in the regions inside and outside the horizon are connected by the changing of the Planck mass sign.

scholarly journals General Relativity with a Positive Cosmological Constant as a Gauge Theory.

2018 ◽  
Author(s):  
Marta Dudek ◽  
Janusz Garecki
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Cosmological Constant ◽  
Gauge Field ◽  
Geometrical Interpretation ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Positive Cosmological Constant

In the paper we show that the general relativity in recent Einstein-Palatini formulation is equivalent to a gauge field. We begin with a bit of information of the Einstein-Palatini formulation and derive Einstein field equations from it. In the next section, we consider general relativity with a positive cosmological constant in terms of the corrected curvature. We show that in terms of the corrected curvature general relativity takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the corrected curvature.

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