关于双曲空间的有效降维
On Effective Dimensional Reduction in Hyperbolic Spaces
摘要：
证明了双曲空间$H^D$中重粒子的经典运动在$D-1$坐标下具有有界性。研究狄拉克方程，发现经典运动的有界性对应于量子问题中费米子在红外区的有效降维$D+1 \to 1+1$.这种有效的降维导致双曲空间中动力学对称破缺的耦合常数的零临界值。
英文摘要：
It is shown that the classical motion of massive particles in hyperbolic spaces $H^D$ 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 $D+1 \to 1+1$ 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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