New Equation of Nonrelativistic Physics and Theory of Dark Matter

TL;DR

The paper derives new Galilean invariant equations, including a novel asymmetric equation proposed as fundamental for dark matter, leading to a theory that explains dark matter properties and predicts detectable gravitational radiation.

Contribution

It introduces a new asymmetric equation for dark matter derived from Galilean group representations, expanding the theoretical framework of nonrelativistic physics.

Findings

The new equation models dark matter properties.

The theory predicts detectable gravitational radiation.

It unifies dark matter and ordinary matter equations.

Abstract

Two infinite sets of Galilean invariant equations are derived using the irreducible representations of the orthochrous extended Galilean group. It is shown that one set contains the Schr\"odinger equation, which is the fundamental equation for ordinary matter, and the other set has a new asymmetric equation, which is proposed to be the fundamental equation for dark matter. Using this new equation, a theory of dark matter is developed and its profound physical implications are discussed. This theory explains the currently known properties of dark matter and also predicts a detectable gravitational radiation.