Noncommutative space-time and Hausdorff dimension

作者：Anjana V^*; Harikumar E; Kapoor A K

来源：International Journal of Modern Physics A, 2017, 32(31): 1750183.

DOI：10.1142/S0217751X17501834

• Hausdorff dimension
• kappa-deformed space-time
• generalized uncertainty relation

We study the Hausdorff dimension of the path of a quantum particle in noncommutative space-time. We show that the Hausdorff dimension depends on the deformation parameter a and the resolution Delta x for both nonrelativistic and relativistic quantum particle. For the nonrelativistic case, it is seen that Hausdorff dimension is always less than 2 in the noncommutative space-time. For relativistic quantum particle, we find the Hausdorff dimension increases with the noncommutative parameter, in contrast to the commutative space-time. We show that noncommutative correction to Dirac equation brings in the spinorial nature of the relativistic wave function into play, unlike in the commutative space-time. By imposing self-similarity condition on the path of nonrelativistic and relativistic quantum particle in noncommutative space-time, we derive the corresponding generalized uncertainty relation.

• 出版日期2017-11-10