Graded Lie Algebroids: A Framework for Geometrization of Matter and Forces Unification

  • Ghodratallah Fasihi Ramandi
  • Naser Boroojerdian
Research Paper


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 \(Z_{2}\)-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.


\(Z_{2}\)-graded Lie algebroid Graded metric Hilbert–Einstein action Unified field equation 


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Copyright information

© Shiraz University 2018

Authors and Affiliations

  • Ghodratallah Fasihi Ramandi
    • 1
  • Naser Boroojerdian
    • 1
  1. 1.Department of Pure Mathematics, Faculty of Mathematics and Computer ScienceAmirkabir University of TechnologyTehranIran

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