Two-point functions in (loop) quantum cosmology

Abstract

The path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories of volume transitions is discussed, with particular but non-exclusive reference to loop quantum cosmology. Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, pointing out the choices involved in their definitions, deriving their vertex expansions and the composition laws they satisfy. We clarify the origin and relations of different quantities previously defined in the literature, in particular the tie between definitions using a group averaging procedure and those in a deparametrized framework. Finally, we draw some conclusions about the physics of a single quantum universe (where there exist superselection rules on positive- and negative-frequency sectors and different choices of inner product are physically equivalent) and multiverse field theories where the role of these sectors and the inner product are reinterpreted.

29 pages; v2: typos corrected, references added

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Cited by in corpus (11)

• Loop Quantum Cosmology: A Status Report
• Introduction to Loop Quantum Cosmology
• Group field cosmology: a cosmological field theory of quantum geometry
• Many-nodes/many-links spinfoam: the homogeneous and isotropic case
• Linking covariant and canonical LQG II: Spin foam projector
• Classical Setting and Effective Dynamics for Spinfoam Cosmology
• Path integral polymer propagator of relativistic and non-relativistic particles
• Path Integrals and Alternative Effective Dynamics in Loop Quantum Cosmology
• Discrete and continuum third quantization of Gravity
• 2-point functions in quantum cosmology
• Cosmological dynamics in spin-foam loop quantum cosmology: challenges and prospects