Fractional Canonical Quantization: a Parallel with Noncommutativity

Adopting a particular approach to fractional calculus, this paper sets out to build up a consistent extension of the Faddeev-Jackiw (or Symplectic) algorithm to carry out the quantization procedure of coarse-grained models in the standard canonical way. In our treatment, we shall work with the Modif...

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Bibliographic Details
Published inInternational journal of theoretical physics Vol. 53; no. 7; pp. 2379 - 2395
Main Authors Godinho, Cresus F. L., Weberszpil, Jose, Helayël Neto, J. A.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.07.2014
Subjects
Elementary Particles
Mathematical and Computational Physics
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Theoretical
Constrained systems
Noncommutativity
Canonical quantization
Fractional calculus
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ISSN0020-7748
1572-9575
DOI10.1007/s10773-014-2037-5

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Summary:Adopting a particular approach to fractional calculus, this paper sets out to build up a consistent extension of the Faddeev-Jackiw (or Symplectic) algorithm to carry out the quantization procedure of coarse-grained models in the standard canonical way. In our treatment, we shall work with the Modified Riemman Liouville (MRL) approach for fractional derivatives, where the chain rule is as efficient as it is in the standard differential calculus. We still present a case where we consider the situation of charged particles moving on a plane with velocity r ̇ , subject to an external and intense magnetic field in a coarse-grained scenario. We propose an interesting parallelism with the noncommutative case.
ISSN:0020-7748
1572-9575
DOI:10.1007/s10773-014-2037-5