Abstract
dc:description.abstractThis thesis constitutes a first attempt to derive aspects of standard model particle physics from little more than an algebra. Here, we argue that physical concepts such as particles, causality, and irreversible time may result from the algebra acting on itself. We then focus on a special case by considering the algebra $\mathbb{R}\otimes\mathbb{C}\otimes\mathbb{H}\otimes\mathbb{O}$. Using nothing more than $\mathbb{R}\otimes\mathbb{C}\otimes\mathbb{H}\otimes\mathbb{O}$ acting on itself, we set out to find standard model particle representations. From the complex quaternionic portion of the algebra, we find generalized ideals, and show that they describe concisely all of the Lorentz representations of the standard model. From the complex octonionic portion of the algebra, we find minimal left ideals, and show that they mirror the behaviour of a generation of quarks and leptons under su(3)c and u(1)em. We then demonstrate a rudimentary electroweak model which yields a straightforward explanation as to why SU(2)L acts only on left-handed states. This holds in the case of leptons. Finally, we demonstrate how $\mathbb{C}\otimes\mathbb{O}$ can generate a 64-$\mathbb{C}$-dimensional algebra, wherein we find the SU(3)c irreducible representations corresponding to three generations of quarks and leptons. We then conclude by showing how to arrive at all 48 electric charges.
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Furey, C
Subjects
dc:subject × 3Rights
dc:rights- Language dc:language
- eng
Identifiers
dc:identifier.*- DOI dc:identifier.doi
- https://doi.org/10.17863/CAM.37465
- OAI identifier oai:identifier
- oai:www.repository.cam.ac.uk:1810/292005