On Effective Dimensional Reduction in Hyperbolic Spaces
Abstract
It is shown that the classical motion of massive particles in hyperbolic spaces HD has a bounded character in D-1 coordinates. Studying the Dirac equation, it is found that a bounded character of the classical motion corresponds to the effective dimensional reduction D+1 1+1 for fermions in the infrared region in the quantum problem. This effective dimensional reduction leads to the zero critical value of coupling constant for dynamical symmetry breaking in hyperbolic spaces.
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