Graded Lie Algebroids: A Framework For Geometrization Of Matter And Forces Unification

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Document Type : Regular Paper

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a Department of Pure Mathematics, PHD student, Amirkabir University of Technology, No. 424, Hafez Ave.

Abstract

In this paper, we introduce a geometric structure that is capable of describing
matter and forces simultaneously. This structure can be established by using
the notion of Z2
-graded Lie algebroid structures and graded semi-Riemannian
metrics on them. Using calculus of variations, we derive field equations
from the extended Hilbert-Einstein action. The derived equations contain
Yang-Mills and Einstein field equations simultaneously. The even part of the
graded Lie algebroid describes forces and its odd part is related to matter
and particles.

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Iranian Journal of Science

Articles in Press, Accepted Manuscript
Available Online from 01 March 2016

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