Abstract
We here propose a 5-dimensional {\bf Abelian gauge} model based on the mixing between a $U(1)$ potential and an Abelian 3-form field by means of a topological mass term. An extended covariant derivative is introduced to minimally couple a Dirac field to the $U(1)$ potential, while this same covariant derivative non-minimally couples the 3-form field to the charged fermion. A number of properties are discussed in 5D; in particular, the appearance of a topological fermionic current. A 4-dimensional reduced version of the model is investigated and, { \bf in addition to the $U(1)$ electric- and magnetic-sort of fields,} there emerges an extra set of electric- and magnetic-like fields which contribute a negative pressure and may be identified as a possible fraction of dark energy. The role of the topological fermionic current is also contemplated upon dimensional reduction from 5D to 4D. Other issues we present in 4 space-time dimensions are the emergence {\bf of a pseudo-scalar massive particle,} an extra massive neutral gauge boson,{\bf which we interpret as a kind of paraphoton}, and the calculation of spin- and velocity-dependent interparticle potentials associated to the exchange of the intermediate bosonic fields of the model.
Highlights
The possibility of a multidimensional Universe has raised a growing interest over the past decades
What we borrow from this correspondence is the point of view that our fundamental physics takes place in 5 space-time dimensions; whether this physics should be analyzed in an Ad S5 or a 5D Minkowski scenario will depend on the particular phenomenon under study
One proposes here to investigate a 5D electromagnetic model with a (Abelian) topological mass term built up in terms of a 1-form and a 3-form gauge potential. Such a description may offer some hint for modeling the so-called dark energy, due to the presence of the 44-component of our energymomentum tensor that may correspond to a negative pressure and may be describing an expanding system
Summary
The possibility of a multidimensional Universe has raised a growing interest over the past decades. In the particular case we are concerned to study, massive gravitons do not couple to the associated fluctuations of the electron and photon due to the fact that they are highly massive, so that, in the energy regime of the validity of the QED processes, those gravitons with so a huge mass (induced by the cosmological constant) are not excited From this perspective, in this paper, we start off from a model based on the association of a 3-form gauge potential with accelerated expansion of the Universe [11]. Our particular model, formulated in 5 space-time dimensions, as already anticipated above, yields, upon a dimensional reduction mechanism, the appearance of an extra neutral massive boson in 4-dimensional Minkowski space [13,14,15] This shall be presented in detail in the sequel.
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