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.

A GAUGE THEORY OF SPIN-1/2 FIELD

1992 ◽  
Vol 07 (33) ◽  
pp. 3053-3057 ◽  
Author(s):  
KAZUNARI SHIMA
Keyword(s):  
Gauge Theory ◽  
Dimensional Space ◽  
Gravitational Interaction ◽  
Space Time ◽  
Dirac Field ◽  
Gauge Invariant ◽  
Dimensional Space Time

A gauge theory of spin-1/2 Dirac field in four-dimensional space-time is presented. The gauge invariant gravitational interaction is also investigated.

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 Dimensionally Compactified Chern-Simon Theory in 5D as a Gravitation Theory in 4D

2017 ◽  
Vol 45 ◽  
pp. 1760005 ◽  
Author(s):  
Ivan Morales ◽  
Bruno Neves ◽  
Zui Oporto ◽  
Olivier Piguet
Keyword(s):  
Dimensional Space ◽  
Cosmological Solution ◽  
Space Time ◽  
Gravitation Theory ◽  
Simons Theory ◽  
De Sitter ◽  
Field Equations ◽  
Sitter Group ◽  
Dimensional Space Time ◽  
Chern Simons

We propose a gravitation theory in 4 dimensional space-time obtained by compacting to 4 dimensions the five dimensional topological Chern-Simons theory with the gauge group SO(1,5) or SO(2,4) – the de Sitter or anti-de Sitter group of 5-dimensional space-time. In the resulting theory, torsion, which is solution of the field equations as in any gravitation theory in the first order formalism, is not necessarily zero. However, a cosmological solution with zero torsion exists, which reproduces the Lambda-CDM cosmological solution of General Relativity. A realistic solution with spherical symmetry is also obtained.

scholarly journals No stable static spherically symmetric wormholes in Horndeski theory

2018 ◽  
Vol 191 ◽  
pp. 07012
Author(s):  
Oleg Evseev ◽  
Oleg Melichev
Keyword(s):  
Scalar Field ◽  
General Theory ◽  
Dimensional Space ◽  
Space Time ◽  
Second Order ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Asymptotically Flat ◽  
Dimensional Space Time

We consider the most general theory of a single scalar field with the second order field equations, the Horndeski theory, in four-dimensional space-time. We show that static, spherically symmetric, asymptotically flat, Lorentzian wormholes are unstable in this theory.

On-shell gauge invariant three-point fermion and boson amplitudes

2020 ◽  
Vol 35 (18) ◽  
pp. 2050085
Author(s):  
Hui Xu
Keyword(s):  
First Principles ◽  
Dimensional Space ◽  
Space Time ◽  
Polynomial Basis ◽  
Gauge Invariant ◽  
Higher Spin ◽  
Dimensional Space Time ◽  
Lagrangian Construction ◽  
Massless Fermions

A polynomial basis for parity-even three-point amplitudes of higher-spin massless fermions and bosons are derived in four-dimensional space–time from first principles. This basis can be used to construct three-point amplitudes of polarizations of any rank. The results are presented using polarization tensors and tensor-spinors, which is convenient when they are applied to Lagrangian construction.

scholarly journals Graviton loop contribution to Higgs potential in gauge-Higgs unification

2020 ◽  
Author(s):  
Yasunari Nishikawa
Keyword(s):  
Gauge Theory ◽  
Higgs Boson ◽  
Quantum Gravity ◽  
Gauge Field ◽  
Effective Potential ◽  
Dimensional Space ◽  
Space Time ◽  
Higgs Potential ◽  
Loop Contribution ◽  
Dimensional Space Time

Abstract We study a two-loop finiteness of an effective potential for a Higgs boson that is the fifth component of a gauge field in an U(1) gauge theory coupled to quantum gravity on the five-dimensional space-time M4 × S1. There are two types of diagrams including quantum gravitational corrections. We find that only one type of diagram contributes to the effective potential for the Higgs boson in fact and its magnitude is finite.

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