Framework, The Physics of sp(2,R)

TL;DR

This paper develops a mathematical framework based on sp(2,R) symmetry that unifies gravity and electromagnetism geometrically, offering potential explanations for dark matter through modified gravity equations.

Contribution

It introduces a novel relativistic quantum field theory framework using sp(2,R) symmetry that unifies fundamental forces and proposes alternative gravity equations.

Findings

Gravity and electromagnetism are unified geometrically.

The source equation for gravity differs from Einstein's, allowing dark matter explanations.

Potential to explain dark matter phenomena through modified gravity equations.

Abstract

A mathematical framework for relativistic quantum field theory is constructed with natural symmetry $\mathsf{so}(2,3)= \mathsf{sp}(2,\mathbb{ R})$. In this framework gravity and electromagnetism unify as aspects of the geometry. The source equation for gravity differs from Einstein's equation and permits behaviour that could explain dark matter.