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- Title
Noncommutative space-time and Hausdorff dimension.
- Authors
Anjana, V.; Harikumar, E.; Kapoor, A. K.
- Abstract
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 and the resolution 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.
- Subjects
SPACETIME; FRACTAL dimensions; QUANTUM theory; NONCOMMUTATIVE function spaces; DIRAC equation
- Publication
International Journal of Modern Physics A: Particles & Fields; Gravitation; Cosmology; Nuclear Physics, 2017, Vol 32, Issue 31, p-1
- ISSN
0217-751X
- Publication type
Article
- DOI
10.1142/S0217751X17501834