2024/12/24 by Kaimakkamis, Eftychios, Partouche, Hervé, Sil, Karunava +1 · 2 citations
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2412.18532
We consider the classical minisuperspace model describing a closed, homogeneous and isotropic Universe, with a positive cosmological constant. Upon canonical quantization, the infinite number of possible operator orderings in the quantum Hamiltonian leads to distinct Wheeler-DeWitt equations for the wavefunction ψ of the Universe. Similarly, ambiguity arises in the path-integral formulation of ψ, due to the infinite choices of path-integral measures for the single degree of freedom of the model. For each choice of path-integral measure, we determine the correct operator ordering of the quantum Hamiltonian and derive the exact form of the Wheeler-DeWitt equation, including all corrections in ℏ. Additionally, we impose Hermiticity of the Hamiltonian to deduce the Hilbert-space measure μ, which appears in the definition of the Hermitian inner product. Remarkably, all quantum predictions can be expressed through the combination Ψ=√μ ψ, which satisfies a universal Wheeler-DeWitt equation, independent of the initial path-integral prescription. This result demonstrates that all seemingly distinct quantum theories arising from different quantization schemes of the same classical model are fundamentally equivalent.