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arXiv · 1305.3421

Mode-sum construction of the two-point functions for the Stueckelberg vector fields in the Poincaré patch of de Sitter space

Markus B. Fröb·Atsushi Higuchi
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Abstract

We perform canonical quantization of the Stueckelberg Lagrangian for massive vector fields in the conformally flat patch of de Sitter space in the Bunch-Davies vacuum and find their Wightman two-point functions by the mode-sum method. We discuss the zero-mass limit of these two-point functions and their limits where the Stueckelberg parameter $ξ$ tends to zero or infinity. It is shown that our results reproduce the standard flat-space propagator in the appropriate limit. We also point out that the classic work of Allen and Jacobson for the two-point function of the Proca field and a recent work by Tsamis and Woodard for that of the transverse vector field are two limits of our two-point function, one for $ξ\to \infty$ and the other for $ξ\to 0$. Thus, these two works are consistent with each other, contrary to the claim by the latter authors.

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Markus B. Fröb, Atsushi Higuchi. 2014-06-03. Mode-sum construction of the two-point functions for the Stueckelberg vector fields in the Poincaré patch of de Sitter space. https://doi.org/10.1063/1.4879496

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