Duru-Kleinert Path Integral in Unimodular Quantum Cosmology
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.
Related
- Matter Creation in Unimodular Gravity Cosmology
- Lifshitz Phase of Quantum Gravity: The Infrared Fixed Point of the (2+1)D Unimodular Hořava-Chern-Simons Model
- Consistency Checks for Λ positive Quantum Cosmology
- Nonequilibrium Apparent-Horizon Thermodynamics in Effective Loop Quantum Cosmology
- Shadow signatures and near-horizon energy accumulation in coherent quantum sine-integral black holes
BibTeX
@misc{guo2026durukleinert,
title = {{Duru-Kleinert Path Integral in Unimodular Quantum Cosmology}},
author = {Xiao-Kan Guo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.18983},
eprint = {2608.18983},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.18983},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Duru-Kleinert Path Integral in Unimodular Quantum Cosmology
AU - Xiao-Kan Guo
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2608.18983
UR - https://arxiv.org/abs/2608.18983
AB - 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.
ER -