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.
Broojerdian, N., & Fasihi Ramandi, G. (2016). Graded Lie Algebroids: A Framework For Geometrization Of Matter And Forces Unification. Iranian Journal of Science, (), -. doi: 10.22099/ijsts.2016.3612
MLA
Naser Broojerdian; Ghodratallah Fasihi Ramandi. "Graded Lie Algebroids: A Framework For Geometrization Of Matter And Forces Unification", Iranian Journal of Science, , , 2016, -. doi: 10.22099/ijsts.2016.3612
HARVARD
Broojerdian, N., Fasihi Ramandi, G. (2016). 'Graded Lie Algebroids: A Framework For Geometrization Of Matter And Forces Unification', Iranian Journal of Science, (), pp. -. doi: 10.22099/ijsts.2016.3612
VANCOUVER
Broojerdian, N., Fasihi Ramandi, G. Graded Lie Algebroids: A Framework For Geometrization Of Matter And Forces Unification. Iranian Journal of Science, 2016; (): -. doi: 10.22099/ijsts.2016.3612