Share This Article:

On q-Deformed Calculus in Quantum Geometry

Abstract Full-Text HTML XML Download Download as PDF (Size:371KB) PP. 1586-1593
DOI: 10.4236/am.2014.510151    3,600 Downloads   4,438 Views   Citations


The relation between noncommutative (or quantum) geometry and themathematics of spacesis in many ways similar to the relation between quantum physicsand classical physics. One moves from the commutative algebra of functions on a space (or a commutative algebra of classical observable in classical physics) to a noncommutative algebra representing a noncommutative space (or a noncommutative algebra of quantum observables in quantum physics). The object of this paper is to study the basic rules governing q-calculus as compared with the classical Newton-Leibnitz calculus.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Maliki, O. and Ugwu, E. (2014) On q-Deformed Calculus in Quantum Geometry. Applied Mathematics, 5, 1586-1593. doi: 10.4236/am.2014.510151.


[1] Connes, A. (1986) Non-Commutative Differential Geometry. Extrait des Publications Mathematiques-IHES, 62. (cited in: Qauntum Principal Bundles and Their Characteristic Classes (pdf), by MICO DURDEVIC, arXiv:q-alg/960505008vi (5 May 1996))
[2] Connes, A. (1994) Noncommutative Geometry. Academic Press, New York.
[3] Brateli, O. and Robinson, D. (1979) Operator Algebras and Quantum Statistical Mechanics, Volumes 1/2. Springer-Verlag, Berlin.
[4] Brown, L.G., Douglas, R.G. and Filmore, P.G. (1977) Extensions of C*-Algebras and K-Homology. Annals of Mathematics, 105, 265-324.
[5] Benaoum, H.B. (1999) (q; h)-Analogue of Newton’s Binomial Formula. Journal of Physics A: Mathematical and General, 32, 2037-2040.
[6] Rosengren, H. (1999) Multivariable Orthogonal Polynomials as Coupling Coefficients for Lie and Quantum Algebra Representations. Dissertation, Centre for Mathematical Sciences, Mathematics (Faculty of Science), Lund, 167.
[7] Kowalski-Glikman, J. (1998) Black Hole Solution of Quantum Gravity. Physics Letters A, 250, 62-66.
[8] Chang, Z. (1999) Quantum Anti-De Sitter Space. (reprint)
[9] Steinacker, H. (1998) Finite Dimensional Unitary Representations of Quantum Antide Sitter Groups at Roots of Unity. Communications in Mathematical Physics, 192, 687-706.

comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.