Year: 2026
Type: preprint
Abstract: The Wheeler-DeWitt equation of a flat Friedmann-Lemaitre-Robertson-Walker universe filled with pressureless dust and a cosmological constant in unimodular gravity reduces, for a specific factor ordering and a specific self-adjoint extension, to the $l=0$ radial Schrödinger equation of a hydrogen atom. We revisit this correspondence from the point of view of the Green's functions and the Duru-Kleinert path integrals. Working directly with the reduced operator on the half-line, we obtain the Green's function in Whittaker form and fix its normalization by a Wronskian argument. Its Gamma-function poles give the reduced-operator spectrum which recovers the quantization of the negative cosmological term. We also perform the operator-level Duru-Kleinert transformation, whose Jacobian generates a barrier which after rescaling is exactly the centrifugal barrier of a two-dimensional oscillator. Retaining it reproduces the Coulomb pole condition. For positive cosmological constant, we give the continuum spectral measure and the Sommerfeld factor.
Source: arXiv (Cornell University)
Author: Guo, Xiao-Kan
Institution: Yancheng Institute of Technology
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Yancheng Institute of Technology
Award: G6835475518
OpenAlex ID: W7203886253