On q-Deformed Calculus in Quantum Geometry
Affiliation(s)
Department of Industrial Mathematics and Applied Statistics, Ebonyi State University, Abakaliki, Nigeria. Department of Industrial Physics, Ebonyi State University, Abakaliki, Nigeria.
Department of Industrial Mathematics and Applied Statistics, Ebonyi State University, Abakaliki, Nigeria. Department of Industrial Physics, Ebonyi State University, Abakaliki, Nigeria.
ABSTRACT
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.
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.
Maliki, O. and Ugwu, E. (2014) On q-Deformed Calculus in Quantum Geometry. Applied Mathematics, 5, 1586-1593. doi: 10.4236/am.2014.510151.
References
[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. http://dx.doi.org/10.2307/1970999 [5] Benaoum, H.B. (1999) (q; h)-Analogue of Newton’s Binomial Formula. Journal of Physics A: Mathematical and General, 32, 2037-2040. http://dx.doi.org/10.1088/0305-4470/32/10/019 [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. http://dx.doi.org/10.1016/S0375-9601(98)00706-3 [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.
http://dx.doi.org/10.1007/s002200050315
[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. http://dx.doi.org/10.2307/1970999 [5] Benaoum, H.B. (1999) (q; h)-Analogue of Newton’s Binomial Formula. Journal of Physics A: Mathematical and General, 32, 2037-2040. http://dx.doi.org/10.1088/0305-4470/32/10/019 [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. http://dx.doi.org/10.1016/S0375-9601(98)00706-3 [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.
http://dx.doi.org/10.1007/s002200050315