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

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