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Graded Lie Algebroids: A Framework For Geometrization Of Matter And Forces Unification | ||
| Iranian Journal of Science | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 11 اسفند 1394 | ||
| نوع مقاله: Regular Paper | ||
| شناسه دیجیتال (DOI): 10.22099/ijsts.2016.3612 | ||
| نویسندگان | ||
| Naser Broojerdian* ؛ Ghodratallah Fasihi Ramandi | ||
| a Department of Pure Mathematics, PHD student, Amirkabir University of Technology, No. 424, Hafez Ave. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Z2-graded Lie Algebroid؛ Graded metric؛ Hilbert-Einstein action؛ Unified Field Equation | ||
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