This paper provides a pedagogical introduction to the physics of extra dimensions by examining the behavior of scalar fields in three landmark models: the ADD, Randall-Sundrum, and DGP spacetimes. Results of this analysis provide qualitative insights into the corresponding behavior of gravitational fields and elementary particles in each of these models. In these “brane world” models, the familiar four dimensional spacetime of everyday experience is called the brane and is a slice through a higher dimensional spacetime called the bulk. The particles and fields of the standard model are assumed to be 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 and the scalar field produced by a static point source located on the brane. For the ADD and Randall-Sundrum models, at large distances, the field looks like that of a point source in four spacetime dimensions, but at short distances, it crosses over to a form appropriate to the higher dimensional spacetime. For the DGP model, the field has the higher dimensional form at long distances rather than short. The behavior of these scalar fields, derived using only undergraduate level mathematics, closely mirror the results that one would obtain by performing the far more difficult task of analyzing the behavior of gravitational fields in these spacetimes.
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May 01 2018
Exploring extra dimensions with scalar fields
Katherine Brown;
Katherine Brown
Department of Physics, Hamilton College
, Clinton, New York
13323
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Harsh Mathur;
Harsh Mathur
a)
Department of Physics, Case Western Reserve University
,
Cleveland, Ohio 44106-7079 a)Author to whom correspondence should be addressed: [email protected].
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Mike Verostek
Mike Verostek
Department of Physics, Hamilton College
, Clinton, New York
13323
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Katherine Brown
Harsh Mathur
a)
Mike Verostek
Department of Physics, Hamilton College
, Clinton, New York
13323
a)Author to whom correspondence should be addressed: [email protected].
Am. J. Phys. 86, 327–337 (2018)
Article history
Received:
June 04 2016
Accepted:
December 09 2017
Citation
Katherine Brown, Harsh Mathur, Mike Verostek; Exploring extra dimensions with scalar fields. Am. J. Phys. 1 May 2018; 86 (5): 327–337. https://doi.org/10.1119/1.5024221
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