On Effective Dimensional Reduction in Hyperbolic Spaces
E.V. Gorbar
TL;DR
This paper demonstrates that classical and quantum behaviors in hyperbolic spaces lead to an effective reduction in dimensionality, impacting fermion dynamics and symmetry breaking phenomena.
Contribution
It reveals a novel link between classical motion bounds and quantum dimensional reduction for fermions in hyperbolic spaces.
Findings
Classical motion in hyperbolic spaces is bounded in D-1 coordinates.
Quantum fermions exhibit effective 1+1 dimensional behavior in the infrared.
Zero critical coupling for dynamical symmetry breaking in hyperbolic spaces.
Abstract
It is shown that the classical motion of massive particles in hyperbolic spaces has a bounded character in coordinates. Studying the Dirac equation, it is found that a bounded character of the classical motion corresponds to the effective dimensional reduction 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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Taxonomy
Topicsadvanced mathematical theories · Mathematical Analysis and Transform Methods · Differential Equations and Boundary Problems