The Scalar Field Kernel in Cosmological Spaces

Details The Scalar Field Kernel in Cosmological Spaces The Scalar Field Kernel in Cosmological Spaces

2007-12-21

arxiv.org/abs/0712.3685v2

Class.Quant.Grav.25:125009,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, 1 figure

Scientific paper

10.1088/0264-9381/25/12/125009

We construct the quantum mechanical evolution operator in the Functional Schrodinger picture - the kernel - for a scalar field in spatially homogeneous FLRW spacetimes when the field is a) free and b) coupled to a spacetime dependent source term. The essential element in the construction is the causal propagator, linked to the commutator of two Heisenberg picture scalar fields. We show that the kernels can be expressed solely in terms of the causal propagator and derivatives of the causal propagator. Furthermore, we show that our kernel reveals the standard light cone structure in FLRW spacetimes. We finally apply the result to Minkowski spacetime, to de Sitter spacetime and calculate the forward time evolution of the vacuum in a general FLRW spacetime.

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