Kaluza-Klein Theories and the Dirac Monopole
Conventional grand unified theories unify the strong interactions with electroweak interactions by postulating that at energy scales of ∼1015 GeV the two interactions become different facets of the same. In a typical scheme of this type, a gauge group G becomes spontaneously broken down to H = SU(3)×SU(2)×U(1) at energies less than the grand unification scale. G is often supposed to be SU(5), although it can in principle be any compact gauge group which contains H. At these very high energies, it seems to be rather difficult to imagine any direct tests of such theories. Nevertheless, there are at least two indirect tests of these ideas. The first is that they predict the existence of baryon-number violating interactions.1 These would give rise to an observable decay of the proton on timescales of the order of 1031±2 years. Such decays have not been observed. One should, however, point out that the observability of large amounts of antimatter in the universe is superficially incompatible with the standard big-bang model (or inflationary models) of the universe unless such baryon-number non-conserving reactions took place in the early universe.2 These would guarantee that only matter would be present in the universe at its current epoch.
KeywordsGauge Group Gauge Field Magnetic Charge Spacetime Dimension Grand Unify Theory
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