Graded Lie Algebroids: A Framework for Geometrization of Matter and Forces Unification
Autor: | Naser Boroojerdian, Ghodratallah Fasihi Ramandi |
---|---|
Rok vydání: | 2018 |
Předmět: |
Lie algebroid
Pure mathematics 021103 operations research Unification General Mathematics 0211 other engineering and technologies Structure (category theory) General Physics and Astronomy 02 engineering and technology General Chemistry 01 natural sciences Action (physics) 0103 physical sciences Einstein field equations General Earth and Planetary Sciences Calculus of variations 010306 general physics General Agricultural and Biological Sciences Field equation Mathematics |
Zdroj: | Iranian Journal of Science and Technology, Transactions A: Science. 42:917-926 |
ISSN: | 2364-1819 1028-6276 |
DOI: | 10.1007/s40995-018-0516-x |
Popis: | 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. |
Databáze: | OpenAIRE |
Externí odkaz: |