Two-point functions in (loop) quantum cosmology

Details Two-point functions in (loop) quantum cosmology Two-point functions in (loop) quantum cosmology

2010-11-18

arxiv.org/abs/1011.4290v2

Class.Quant.Grav.28:125014,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

29 pages; v2: typos corrected, references added

Scientific paper

10.1088/0264-9381/28/12/125014

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.

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