Novel Complete Non-compact Symmetries for the Wheeler-DeWitt Equation in a Wormhole Scalar Model and Axion-Dilaton String Cosmology

TL;DR

This paper uncovers hidden symmetries in the Wheeler-DeWitt equation for wormhole and string cosmology models, revealing new solutions and symmetry structures that deepen understanding of quantum cosmological states.

Contribution

It identifies full symmetry groups of the Wheeler-DeWitt equation in specific models and introduces new wormhole solutions, highlighting the role of hidden symmetries in quantum cosmology.

Findings

U(1,1) symmetry in Hawking-Page model

U(2,1) symmetry in axion-dilaton cosmology

Existence of SL(2,R) dynamical symmetry with matter-energy renormalization

Abstract

We find the full symmetries of the Wheeler-DeWitt equation for the Hawking and Page wormhole model and an axion-dilaton string cosmology. We show that the Wheeler-DeWitt Hamiltonian admits an U(1,1) hidden symmetry for the Hawking and Page model and U(2,1) for the axion-dilaton string cosmology. If we consider the existence of matter-energy renormalization, for each of these models we find that the Wheeler-DeWitt Hamiltonian accept an additional SL(2,R) dynamical symmetry. In this case, we show that the SL(2,R) dynamical symmetry generators transform the states from one energy Hilbert eigensubspace to another. Some new wormhole type-solutions for both models are found.