Physics#Quantum Cosmology, Wheeler-DeWitt Equation, Operator Ordering, Path Integral🔬 ResearchAnalyzed: Jan 3, 2026 18:31
Ordering-Independent Quantum Cosmology
Published:Dec 29, 2025 18:08
•1 min read
•ArXiv
Analysis
This paper addresses the ordering ambiguity problem in the Wheeler-DeWitt equation, a central issue in quantum cosmology. It demonstrates that for specific minisuperspace models, different operator orderings, which typically lead to different quantum theories, are actually equivalent and define the same physics. This is a significant finding because it simplifies the quantization process and provides a deeper understanding of the relationship between path integrals, operator orderings, and physical observables in quantum gravity.
Key Takeaways
- •Demonstrates the equivalence of different operator orderings in the Wheeler-DeWitt equation for specific minisuperspace models.
- •Establishes a direct link between path-integral measures, operator orderings, and physical observables.
- •Provides a framework for constructing a consistent quantum theory in these models, independent of operator ordering.
- •Illustrates the formalism with applications to de Sitter Jackiw-Teitelboim gravity and the Starobinsky model.
Reference
“The consistent orderings are in one-to-one correspondence with the Jacobians associated with all field redefinitions of a set of canonical degrees of freedom. For each admissible operator ordering--or equivalently, each path-integral measure--we identify a definite, positive Hilbert-space inner product. All such prescriptions define the same quantum theory, in the sense that they lead to identical physical observables.”