Teleparallel Lagrange geometry and a unified field theory

In this paper, we construct a field theory unifying gravity and electromagnetism in the context of extended absolute parallelism (EAP) geometry. This geometry combines, within its structure, the geometric richness of the tangent bundle and the mathematical simplicity of absolute parallelism (AP) geo...

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Bibliographic Details
Published in:Classical and quantum gravity 2010-02, Vol.27 (4), p.045005-045005
Main Authors: Wanas, M I, Youssef, Nabil L, Sid-Ahmed, A M
Format: Article
Language:English
Subjects:
Construction
Electromagnetic fields
Field theory
Horizontal
Mathematical analysis
Quantum gravity
Scalars
Unified field theory
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Summary:In this paper, we construct a field theory unifying gravity and electromagnetism in the context of extended absolute parallelism (EAP) geometry. This geometry combines, within its structure, the geometric richness of the tangent bundle and the mathematical simplicity of absolute parallelism (AP) geometry. The constructed field theory is a generalization of the generalized field theory (GFT) formulated by Mikhail and Wanas. The theory obtained is purely geometric. The horizontal (resp. vertical) field equations are derived by applying the Euler--Lagrange equations to an appropriate horizontal (resp. vertical) scalar Lagrangian. The symmetric part of the resulting horizontal (resp. vertical) field equations gives rise to a generalized form of Einstein's field equations in which the horizontal (resp. vertical) energy--momentum tensor is purely geometric. The skew-symmetric part of the resulting horizontal (resp. vertical) field equations gives rise to a generalized form of Maxwell equations in which the electromagnetic field is purely geometric. Some interesting special cases, which reveal the role of the nonlinear connection in the obtained field equations, are examined. Finally, the condition under which our constructed field equations reduce to the GFT is explicitly established.
ISSN:0264-9381
DOI:10.1088/0264-9381/27/4/045005