Extended-Lorentz Quantum-Cosmology Symmetry Group

TL;DR

This paper introduces an extended-Lorentz symmetry group in quantum cosmology, unifying conserved attributes of the Milne quantum-universe and defining universe evolution through a novel age-dependent Hamiltonian.

Contribution

It defines a 9-parameter extended-Lorentz Lie group with conserved attributes and demonstrates its invariance properties, including universe age and Hamiltonian, in quantum cosmology.

Findings

The symmetry group unifies conserved quantum attributes.

Universe age remains invariant under the symmetry group.

An age-dependent Hamiltonian generates universe evolution.

Abstract

Unitarily representable by transformations of Milne quantum-universe (MQU) Hilbert-space vectors is a 9-parameter 'extended-Lorentz' Lie group whose algebra comprises 9 conserved MQU-constituent ('quc') attributes: electric charge, energy, spirality, 3-vector momentum and 3-vector angular momentum. Commutation with the full symmetry algebra by the 3-element Lorentz-extending sub-algebra identifies any quc by its (permanent) trio of charge, spirality and energy integers. Milne's redshift-specifying 'universe age' is invariant under the MQU symmetry group. Also invariant is the (elsewhere specified) universe hamiltonian--a self-adjoint age-dependent Hilbert-space operator (not a symmetry-algebra member) that generates universe evolution with increasing age through a 'Schrodinger' (first-order) differential equation.