Monogenic functions in 5-dimensional spacetime used as first principle: gravitational dynamics, electromagnetism and quantum mechanics

TL;DR

This paper explores monogenic functions in 5D spacetime's geometric algebra to derive fundamental physics laws, including relativistic dynamics, electromagnetism, and quantum mechanics, offering a novel mathematical approach.

Contribution

It introduces a new framework using monogenic functions in 5D spacetime to derive key physical laws, extending traditional theories with a geometric algebra approach.

Findings

Derivation of Maxwell's equations from monogenic functions

Generation of relativistic dynamics differing from Einstein's theory

Connection between Euclidean and Minkowski spaces via monogenic functions

Abstract

Monogenic functions are functions of null vector derivative and are here analysed in the geometric algebra of 5-dimensional spacetime, G(4,1), in order to derive several laws of fundamental physics. The paper introduces the working algebra and the definition of monogenic functions, showing that these generate two 4-dimensional spaces, one with Euclidean signature and the other one with Minkowski signature. The equivalence conditions between the two spaces are studied and relativistic dynamics, not entirely coincident with Einstein's general theory of relativity, is demonstrated. The monogenic condition is then shown to produce Maxwell's equations and electrodynamics both classical and quantized.