scholarly journals Covariant Field Equations in Supergravity

2017 ◽  
Vol 65 (12) ◽  
pp. 1700071 ◽  
Author(s):  
Bram Vanhecke ◽  
Antoine Van Proeyen
Keyword(s):  
Field Equations ◽  
Covariant Field

scholarly journals The unitary representations of the Poincar\'e group in any spacetime dimension

2021 ◽  
Author(s):  
Xavier Bekaert ◽  
Nicolas Boulanger
Keyword(s):  
Arbitrary Dimension ◽  
Minkowski Spacetime ◽  
Irreducible Representations ◽  
Theoretical Treatment ◽  
Spacetime Dimension ◽  
Field Equations ◽  
Negative Mass ◽  
Relativistic Field ◽  
Fundamental Particles ◽  
Covariant Field

An extensive group-theoretical treatment of linear relativistic field equations on Minkowski spacetime of arbitrary dimension D\geqslant 3D≥3 is presented. An exhaustive treatment is performed of the two most important classes of unitary irreducible representations of the Poincar'e group, corresponding to massive and massless fundamental particles. Covariant field equations are given for each unitary irreducible representation of the Poincar'e group with non-negative mass-squared.

scholarly journals NONLINEAR REALIZATION OF THE LOCAL CONFORM-AFFINE SYMMETRY GROUP FOR GRAVITY IN THE COMPOSITE FIBER BUNDLE FORMALISM

2007 ◽  
Vol 04 (06) ◽  
pp. 1041-1074 ◽  
Author(s):  
S. A. ALI ◽  
S. CAPOZZIELLO
Keyword(s):  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Composite Fiber ◽  
Field Equations ◽  
Nonlinear Realization ◽  
Covariant Derivatives ◽  
Affine Symmetry ◽  
Symmetry Transformations ◽  
Covariant Field ◽  
Gauge Theory Of Gravity

A gauge theory of gravity based on a nonlinear realization (NLR) of the local Conform-Affine (CA) group of symmetry transformations is presented. The coframe fields and gauge connections of the theory are obtained. The tetrads and Lorentz group metric are used to induce a spacetime metric. The inhomogenously transforming (under the Lorentz group) connection coefficients serve as gravitational gauge potentials used to define covariant derivatives accommodating minimal coupling of matter and gauge fields. On the other hand, the tensor valued connection forms serve as auxiliary dynamical fields associated with the dilation, special conformal and deformational (shear) degrees of freedom inherent in the bundle manifold. The bundle curvature of the theory is determined. Boundary topological invariants are constructed. They serve as a prototype (source free) gravitational Lagrangian. The Bianchi identities, covariant field equations and gauge currents are obtained.

scholarly journals Unification Principle and a Geometric Field Theory

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Mamdouh I. Wanas ◽  
Samah N. Osman ◽  
Reham I. El-Kholy
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Material Distribution ◽  
Curvature Scalar ◽  
Field Equations ◽  
Differential Identity ◽  
Torsion Scalar ◽  
Covariant Field

AbstractIn the context of the geometrization philosophy, a covariant field theory is constructed. The theory satisfies the unification principle. The field equations of the theory are constructed depending on a general differential identity in the geometry used. The Lagrangian scalar used in the formalism is neither curvature scalar nor torsion scalar, but an alloy made of both, the W-scalar. The physical contents of the theory are explored depending on different methods. The analysis shows that the theory is capable of dealing with gravity, electromagnetism and material distribution with possible mutual interactions. The theory is shown to cover the domain of general relativity under certain conditions.

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