Comparison of group-theoretical strategies for unification of 3+1 structures in physics

TL;DR

This paper compares successful and unsuccessful 3+1 unifications in physics using group theory to understand their differences and explore new approaches for unification in particle physics.

Contribution

It analyzes various 3+1 unifications in physics and proposes applying successful group-theoretical methods to improve less successful models.

Findings

Successful unifications often rely on specific group-theoretical structures

Applying methods from successful models may enhance unification attempts

Insights could potentially resolve current theoretical challenges in particle physics

Abstract

One of the most important advances in our understanding of the physical world arose from the unification of 3-dimensional space with 1-dimensional time into a 4-dimensional spacetime. Many other physical concepts also arise in similar 3+1 relationships, and attempts have been made to unify some of these also. Examples in particle physics include the three intermediate vector bosons of the weak interaction, and the single photon of electromagnetism. The accepted unification in this case is the Glashow-Weinberg-Salam model of electro-weak interactions, which forms part of the standard model. Another example is the three colours of quarks and one of leptons. In this case, the Pati-Salam model attempts the unification, but is not currently part of the accepted standard model. I investigate these and other instances of 3+1=4 in fundamental physics, to see if a comparison between the successful and unsuccessful unifications can throw some light on why some succeed and others fail. In particular, I suggest that applying the group-theoretical methods of the more successful unifications to the less successful ones could potentially break the logjam in theoretical particle physics.