Abstract
The general plane wave solutions of the Proca field in conformal charts of the de Sitter expanding universe are derived for arbitrary polarizations showing how the frequencies can be separated in rest frames, defining thus the rest frame vacuum of this field.
Highlights
The general plane wave solutions of the Proca field in conformal charts of the de Sitter expanding universe are derived for arbitrary polarizations showing how the frequencies can be separated in rest frames, defining the rest frame vacuum of this field
In the actual quantum field theory (QFT) on curved backgrounds, the quantum modes of the Proca field [1] (i. e. the massive charged vector field) on the de Sitter space-time are less studied since the method of the maximally symmetric two-point functions [2,3] opened an optimistic alternative horizon promising to avoid the difficulties of manipulating quantum modes
We know so far only the spherical modes derived in spherically symmetric static charts [4] and our plane wave solutions of the momentumhelicity basis [5] we have derived in the co-moving chart of conformal time of the expanding portion of the (1 + 3)dimensional de Sitter space-time
Summary
In the actual quantum field theory (QFT) on curved backgrounds, the quantum modes of the Proca field [1] (i. e. the massive charged vector field) on the de Sitter space-time are less studied since the method of the maximally symmetric two-point functions [2,3] opened an optimistic alternative horizon promising to avoid the difficulties of manipulating quantum modes. The principal problem of the plane waves on the de Sitter manifold is the frequencies separation for any massive field, regardless its spin This comes from the fact that the plane wave mode functions are eigenfunctions of the momentum operator which does not commute with the energy operator that might determine the frequency as the sign of its eigenvalue. In this paper we would like to complete this collection with the rest frame vacuum of the Proca field, determining the mode functions of given momentum which become energy eigenstates in the rest frames For this purpose we need to know the most general form of the vector plane waves with any polarization but this is not studied till since only the helicity basis was used in applications.
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