The Scalar Field Kernel in Cosmological Spaces
arXiv:0712.3685 · doi:10.1088/0264-9381/25/12/125009
Abstract
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.
13 pages, 1 figure
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- Bonus Properties of States of Low Energy
- Functional formulation of quantum theory of a scalar field in a metric with Lorentzian and Euclidean signatures
- Schrödinger evolution of a scalar field in Riemannian and pseudoRiemannian expanding metrics