Abstract
We study the quantum theory of the mass-less vector fields on the Rindler space. We evaluate the Bogoliubov coefficients by means of a new technique based upon the use of light-front coordinates and Mellin transform. We briefly comment about the ensuing Unruh effect and its consequences.
Highlights
The production, propagation and detection of real photons in a non-inertial reference frame are a highly nontrivial subject [1] [2]
The matter is that, if one aims to describe those features in a coordinate independent way, i.e. local diffeomorphism invariant in the physical 3 + 1 dimensional space-time, one has to properly separate the physical and nonphysical polarization modes, the latter ones being necessarily present in any gauge and diffeomorphism invariant general formulation of the quantum theory: this becomes a hard task which has not yet been reached, even for a uniformly accelerated frame in a flat space-time referred to a curved coordinate system [3]
In the nearly whole literature on the non-inertial effects on quantum fields, just like the celebrated Unruh effect [4], or about quantum field theory in curved spaces, the emphasis, examples and applications are always centered around the real scalar field case [4]-[9] up to some few exceptions concerning the realistic electromagnetic or Proca vector fields [10]-[12] or the Dirac and Majorana spinor fields [13] [14]
Summary
The production, propagation and detection of real photons in a non-inertial reference frame are a highly nontrivial subject [1] [2]. It turns out that the correct canonical quantization [15] of the radiation field is not properly taken into account so that, some fictitious singularities appear, which are an artifact of the too drastic simplification of the radiation dynamics in an accelerated reference frame hitherto employed. It is the aim of the present short note to fill this lack and to provide a fully consistent Lorentz and gauge invariant quantum theory for the lineal, i.e. on a one dimensional spatial real line, radiation field. Thanks to the present contribution, the quite relevant and interesting operational analysis developed in [2] is set on a firm and reliable framework and might become seminal for some future experimental verification
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