Quantized Fields \`a la Clifford and Unification

TL;DR

This paper demonstrates that Clifford algebra generators can act as creation and annihilation operators for particles and extended objects, potentially explaining the Standard Model particles and dark matter within a unified algebraic framework.

Contribution

It introduces a novel approach where Clifford algebra generators encode fermions, bosons, and extended objects, linking algebraic structures to particle physics and spacetime geometry.

Findings

Clifford algebra generators behave as creation and annihilation operators.

A quarter of the Clifford algebra basis elements can represent all first-generation Standard Model particles.

Remaining basis elements may correspond to dark matter.

Abstract

It is shown that the generators of Clifford algebras behave as creation and annihilation operators for fermions and bosons. They can create extended objects, such as strings and branes, and can induce curved metric of our spacetime. At a fixed point, we consider the Clifford algebra $Cl(8)$ of the 8-dimensional phase space, and show that one quarter of the basis elements of $Cl(8)$ can represent all known particles of the first generation of the Standard model, whereas the other three quarters are invisible to us and can thus correspond to dark matter.