Could Octonions be the key to the unification of four forces

Shikha, Divya (2022) Could Octonions be the key to the unification of four forces. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Divya Shikha (17MS158)) 17MS158_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (587kB)

Abstract

Spinors are mathematical objects used in physics mainly for defining fermions. The spaces on which Clifford algebras operate are called ‘Spinor spaces’, and their elements are called ‘Spinors’. In quantum field theory, Dirac spinors can be constructed from the clifford algebra Cℓ(4) which can be generated by quaternions as the minimal left ideals of a Clifford algebra. Construction of spinors from the algebra of C⊗O which represents Cℓ(4) gives us one full generation of quarks and leptons while the symmetries gives us bosons along with the standard model gauge group. The works of T.P. Singh regarding a unified description of all forces results in an octonionic spacetime which further justifies the octonionic representation of the standard model.

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