A gauge theory of the Weyl group

1974 ◽  
Vol 340 (1622) ◽  
pp. 249-262 ◽  
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Conservation Laws ◽  
Weyl Group ◽  
Lorentz Group ◽  
Space Time ◽  
Gauge Fields ◽  
Field Equations ◽  
Covariant Derivatives ◽  
The World

The construction of field theory which exhibits invariance under the Weyl group with parameters dependent on space–time is discussed. The method is that used by Utiyama for the Lorentz group and by Kibble for the Poincaré group. The need to construct world-covariant derivatives necessitates the introduction of three sets of gauge fields which provide a local affine connexion and a vierbein system. The geometrical implications are explored; the world geometry has an affine connexion which is not symmetric but is semi-metric. A possible choice of Lagrangian for the gauge fields is presented, and the resulting field equations and conservation laws discussed.

scholarly journals ON THE KALUZA–KLEIN GEOMETRIZATION OF THE ELECTROWEAK MODEL WITHIN A GAUGE THEORY OF THE FIVE-DIMENSIONAL LORENTZ GROUP

2006 ◽  
Vol 15 (05) ◽  
pp. 717-736
Author(s):  
ORCHIDEA MARIA LECIAN ◽  
GIOVANNI MONTANI
Keyword(s):  
Gauge Theory ◽  
Lorentz Group ◽  
Lagrangian Density ◽  
Gauge Fields ◽  
Normalization Factor ◽  
Current Term ◽  
Electroweak Model ◽  
Kaluza Klein

The geometrization of the Electroweak Model is achieved in a five-dimensional Riemann–Cartan framework. Matter spinorial fields are extended to 5 dimensions by the choice of a proper dependence on the extracoordinate and of a normalization factor. U (1) weak hypercharge gauge fields are obtained from a Kaluza–Klein scheme, while the tetradic projections of the extradimensional contortion fields are interpreted as SU (2) weak isospin gauge fields. SU (2) generators are derived by the identification of the weak isospin current to the extradimensional current term in the Lagrangian density of the local Lorentz group. The geometrized U (1) and SU (2) groups will provide the proper transformation laws for bosonic and spinorial fields. Spin connections will be found to be purely Riemannian.

DESITTER GAUGE THEORY OF GRAVITATION

2003 ◽  
Vol 14 (01) ◽  
pp. 41-48 ◽  
Author(s):  
G. ZET ◽  
V. MANTA ◽  
S. BABETI
Keyword(s):  
Gauge Theory ◽  
Riemann Tensor ◽  
Space Time ◽  
Point Of View ◽  
Field Equations ◽  
Minkowski Space Time ◽  
Strength Tensor ◽  
Group A ◽  
Theory Of Gravitation ◽  
Tensor Formula

A deSitter gauge theory of gravitation over a spherical symmetric Minkowski space–time is developed. The "passive" point of view is adapted, i.e., the space–time coordinates are not affected by group transformations; only the fields change under the action of the symmetry group. A particular ansatz for the gauge fields is chosen and the components of the strength tensor are computed. An analytical solution of Schwarzschild–deSitter type is obtained in the case of null torsion. It is concluded that the deSitter group can be considered as a "passive" gauge symmetry for gravitation. Because of their complexity, all the calculations, inclusive of the integration of the field equations, are performed using an analytical program conceived in GRTensorII for MapleV. The program allows one to compute (without using a metric) the strength tensor [Formula: see text], Riemann tensor [Formula: see text], Ricci tensor [Formula: see text], curvature scalar [Formula: see text], field equations, and the integration of these equations.

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 ON THE CORRESPONDENCE BETWEEN NONCOMMUTATIVE FIELD THEORY AND GRAVITY

2007 ◽  
Vol 22 (16) ◽  
pp. 1119-1132 ◽  
Author(s):  
HYUN SEOK YANG
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Gauge Fields ◽  
Noncommutative Field Theory ◽  
Basic Reason ◽  
New Development ◽  
Collective Phenomenon ◽  
Darboux Theorem ◽  
Theory Of Gravity

In this brief review, we summarize the new development on the correspondence between noncommutative (NC) field theory and gravity, shortly referred to as the NCFT/Gravity correspondence. We elucidate why a gauge theory in NC spacetime should be a theory of gravity. A basic reason for the NCFT/Gravity correspondence is that the Λ-symmetry (or B-field transformations) in NC spacetime can be considered as a par with diffeomorphisms, which results from the Darboux theorem. This fact leads to a striking picture about gravity: Gravity can emerge from a gauge theory in NC spacetime. Gravity is then a collective phenomenon emerging from gauge fields living in fuzzy spacetime.

U(2) GAUGE THEORY ON NONCOMMUTATIVE GEOMETRY

2009 ◽  
Vol 24 (15) ◽  
pp. 2889-2897
Author(s):  
G. ZET
Keyword(s):  
Gauge Theory ◽  
Equations Of Motion ◽  
Local Symmetry ◽  
Noncommutative Space ◽  
Gauge Fields ◽  
Zeroth Order ◽  
Field Equations ◽  
Relativistic Analog ◽  
Analog Form ◽  
General Relativistic

We develop a model of gauge theory with U (2) as local symmetry group over a noncommutative space-time. The integral of the action is written considering a gauge field coupled with a Higgs multiplet. The gauge fields are calculated up to the second order in the noncommutativity parameter using the equations of motion and Seiberg-Witten map. The solutions are determined order by order supposing that in zeroth-order they have a general relativistic analog form. The Wu-Yang ansatz for the gauge fields is used to solve the field equations. Some comments on the quantization of the electrical and magnetical charges are also given, with a comparison between commutative and noncommutative cases.

EXACT SOLUTIONS FOR SELF-DUAL SU(2) GAUGE THEORY WITH AXIAL SYMMETRY

2001 ◽  
Vol 16 (11) ◽  
pp. 685-692 ◽  
Author(s):  
G. ZET ◽  
V. MANTA ◽  
C. BANDAC
Keyword(s):  
Gauge Theory ◽  
Axial Symmetry ◽  
Dimensional Space ◽  
Space Time ◽  
Field Equations ◽  
Metric Tensor ◽  
Gauge Invariant ◽  
Local Gauge ◽  
Dimensional Space Time ◽  
Strength Tensor

A model of SU(2) gauge theory is constructed in terms of local gauge-invariant variables defined over a four-dimensional space–time endowed with axial symmetry. A metric tensor gμν is defined starting with the components [Formula: see text] of the strength tensor and its dual [Formula: see text]. The components gμν are interpreted as new local gauge-invariant variables. Imposing the condition that the new metric coincides with the initial metric we obtain the field equations for the considered ansatz. We obtain the same field equations using the condition of self-duality. It is concluded that the self-dual variables are compatible with the axial symmetry of the space–time. A family of analytical solutions of the gauge field equations is also obtained. The solutions have the confining properties. All the calculations are performed using the GRTensorII computer algebra package, running on the MapleV platform.

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.

EXACT SOLUTIONS OF THE SELF-DUALITY EQUATIONS ON THE MINKOWSKI SPACE-TIME

2001 ◽  
Vol 12 (06) ◽  
pp. 801-806 ◽  
Author(s):  
V. MANTA ◽  
G. ZET
Keyword(s):  
Gauge Theory ◽  
Exact Solutions ◽  
Minkowski Space ◽  
Space Time ◽  
The Self ◽  
Gauge Fields ◽  
Self Duality ◽  
Minkowski Space Time ◽  
Dynamical Type ◽  
Analytical Program

A SU(2) Gauge Theory with spherical symmetry over the Minkowski space-time is considered. The self-duality equation of the gauge fields are written and their solutions are obtained. Two exact solutions, one of which is statical and another of dynamical type are given. All the calculations are performed using an analytical program written in GRTensor computer algebra package, which runs on the MapleV platform.

A SUPERSPACE OF (1, 1/2)+(1/2, 1) FERMIONIC COORDINATES

1990 ◽  
Vol 05 (19) ◽  
pp. 3801-3809
Author(s):  
CHRISTOPHER PILOT ◽  
SUBHASH RAJPOOT
Keyword(s):  
Minkowski Space ◽  
Lorentz Group ◽  
Space Time ◽  
Time Coordinate ◽  
Covariant Derivatives ◽  
Minkowski Space Time

A superspace is constructed in which the elements of the superspace consist of the four Minkowski space-time coordinates and a set of vector-spinor coordinates that belong to the irreducible (1, 1/2)+(1/2, 1) representation of the Lorentz group. It is shown that a translation in the vector-spinor coordinates leads to a vector-spinor coordinate dependent translation in the space-time coordinate xμ. The super covariant derivatives are also constructed.

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