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Mode-sum construction of the two-point functions for the Stueckelberg vector fields in the Poincaré patch of de Sitter space. (English) Zbl 1294.81135
Summary: 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 {$$\xi$$} 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 B. Allen and T. Jacobson [Commun. Math. Phys. 103, 669–692 (1986; Zbl 0632.53060)] for the two-point function of the Proca field and a recent work by N. C. Tsamis and R. P. Woodard [J. Math. Phys. 48, No. 5, 052306, 14 p. (2007; Zbl 1144.81417)] for that of the transverse vector field are two limits of our two-point function, one for $$\xi \to \infty$$ and the other for $$\xi \to 0$$. Thus, these two works are consistent with each other, contrary to the claim by the latter authors.{