Mathematics – Logic
Scientific paper
Aug 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007jena.confe..75a&link_type=abstract
"JENAM-2007, "Our non-stable Universe", held 20-25 August 2007 in Yerevan, Armenia. Abstract book, p. 75-75"
Mathematics
Logic
Scientific paper
One of the most important cases that always has been in attention by the physicists is to find a comprehensive theory that singly formulates the natural four interactions. In this direction, the Kaluza-Klein theory was the first theory that could unify gravity and electromagnetism. This theory is obtained by extension of four dimensional Albert Einstein's general relativity to a five dimensional manifold. Theodor Kaluza pointed out that if general relativity theory is extended to a five-dimensional space-time, the equations can be separated out into ordinary four-dimensional gravitation and an extra set of equations which is equivalent to Maxwell's equations for the electromagnetic field, plus an extra field known as the dilation. But, the purely geometrical Kaluza-Klein theory is inconsistent. It leads to an action unbounded from below and thus is unstable. This can be solved by adding an extra real scalar field using the conformal transformation. In this review, besides studying Kaluza-Klein theory, we investigate the conformal transformation and conformal invariance about cosmological consequents of Kaluza-Klein theory and conclude when the five dimensions Kaluza-Klein theory reduces to a four dimensional manifold, a conformal transformation is necessary until the Einstein's equations are obtained.
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