Coherent State Functional Integral in Loop Quantum Cosmology: Alternative Dynamics

Abstract

Coherent state functional integral for the minisuperspace model of loop quantum cosmology is studied. By the well-established canonical theory, the transition amplitude in the path integral representation of loop quantum cosmology with alternative dynamics can be formulated through group averaging. The effective action and Hamiltonian with higher-order quantum corrections are thus obtained. It turns out that for a non-symmetric Hamiltonian constraint operator, the Moyal (star)-product emerges naturally in the effective Hamiltonian. For the corresponding symmetric Hamiltonian operator, the resulted effective theory implies a possible quantum cosmological effect in large scale limit in the alternative dynamical scenario, which coincides with the result in canonical approach. Moreover, the first-order modified Friedmann equation still contains the particular information of alternative dynamics and hence admits the possible phenomenological distinction between the different proposals of quantum dynamics.

10 pages. arXiv admin note: substantial text overlap with arXiv:1110.5480

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Cited by in corpus (17)

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• Path integral polymer propagator of relativistic and non-relativistic particles
• Noether's Charge in the Super-Group Field Cosmology
• Twisted Geometries Coherent States for Loop Quantum Gravity
• Higher dimensional Loop Quantum Cosmology
• Anomaly freedom in perturbative models of Euclidean loop quantum gravity
• Nilpotent Symmetries in Super-Group Field Cosmology
• Factor ordering and large-volume dynamics in quantum cosmology
• Loop quantum modified gravity and its cosmological application
• The effective dynamics of weak coupling loop quantum gravity
• Anomaly freedom of the vector modes with holonomy corrections in perturbative Euclidean loop quantum gravity
• Gravitational waves with generalized holonomy corrections
• Super-group field cosmology in Batalin-Vilkovisky formulation
• Loop quantum cosmology in 2+1 dimension
• Renormalizability of Supersymmetric Group Field Cosmology