This paper provides a pedagogical introduction to the physics of extra dimensions byexamining the behavior of scalar fields in three landmark models: the ADD,Randall-Sundrum, and DGP spacetimes. Results of this analysis provide qualitative insightsinto the corresponding behavior of gravitational fields and elementary particles in eachof these models. In these “brane world” models, the familiar four dimensional spacetime ofeveryday experience is called the brane and is a slice through a higher dimensionalspacetime called the bulk. The particles and fields of the standard model are assumed tobe confined to the brane, while gravitational fields are assumed to propagate in the bulk.For all three spacetimes, we calculate the spectrum of propagating scalar wave modes andthe scalar field produced by a static point source located on the brane. For the ADD andRandall-Sundrum models, at large distances, the field looks like that of a point source infour spacetime dimensions, but at short distances, it crosses over to a form appropriateto the higher dimensional spacetime. For the DGP model, the field has the higherdimensional form at long distances rather than short. The behavior of these scalar fields,derived using only undergraduate level mathematics, closely mirror the results that onewould obtain by performing the far more difficult task of analyzing the behavior ofgravitational fields in these spacetimes.
American Journal of Physics – American Association of Physics Teachers
Published: May 4, 2018
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