Coherent State Functional Integrals in Quantum Cosmology

TL;DR

This paper develops coherent state path integrals for quantum cosmology models, deriving effective actions with quantum corrections and revealing the role of star-products, suggesting potential large-scale quantum effects in the universe.

Contribution

It introduces a unified approach to derive effective Hamiltonians in quantum cosmology using coherent state path integrals and highlights the natural emergence of star-products in the process.

Findings

Effective Hamiltonians with quantum corrections are obtained.

Star-product naturally appears in non-symmetric Hamiltonian cases.

Potential quantum effects at large cosmological scales are suggested.

Abstract

Coherent state functional integrals for the minisuperspace models of quantum cosmology are studied. By the well-established canonical theories, the transition amplitudes in the path-integral representations of Wheeler-DeWitt quantum cosmology and loop quantum cosmology can be formulated through group averaging. The effective action and Hamiltonian with higher-order quantum corrections are thus obtained in both models. It turns out that for a non-symmetric Hamiltonian constraint operator, the Moyal (star)-product emerges naturally in the effective Hamiltonian. This reveals the intrinsic relation among coherent state functional integral, effective theory and star-product. Moreover, both the resulted effective theories imply a possible quantum cosmological effect in large scale limit.