Trace dynamics, and a ground state in spontaneous quantum gravity

TL;DR

This paper develops a trace dynamics framework unifying gravity, gauge fields, and fermions at the Planck scale, deriving a Schrödinger-like eigenvalue equation, and proposing a ground state for spontaneous quantum gravity relevant to early universe cosmology.

Contribution

It introduces a novel Lagrangian for the aikyon, unifying fundamental interactions, and derives an eigenvalue equation with implications for standard model parameters and quantum cosmology.

Findings

Eigenvalue equation analogous to Schrödinger's equation derived.

Fundamental frequency times Planck's constant characterizes energy eigenvalues.

A proposed ground state may describe a non-singular initial epoch in quantum cosmology.

Abstract

We have recently proposed a Lagrangian in trace dynamics, to describe a possible unification of gravity, Yang-Mills fields, and fermions, at the Planck scale. This Lagrangian for the unified entity - called the aikyon - is invariant under global unitary transformations, and as a result possesses a novel conserved charge, known as the Adler-Millard charge. In the present paper, we derive an eigenvalue equation, analogous to the time-independent Schr\"{o}dinger equation, for the Hamiltonian of the theory. We show that in the emergent quantum theory, the energy eigenvalues of the aikyon are characterised in terms of a fundamental frequency times Planck's constant. The eigenvalues of this equation can, in principle, determine the values of the parameters of the standard model. We also report a ground state, in this theory of spontaneous quantum gravity, which could characterise a non-singular initial epoch in quantum cosmology.