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Publications Influence

HIGHER ORDER MEASURES, GENERALIZED QUANTUM MECHANICS AND HOPF ALGEBRAS

- C. Chryssomalakos, M. Durdevich
- Physics, Mathematics
- 10 September 2003

We study Sorkin's proposal of a generalization of quantum mechanics and find that the theories proposed derive their probabilities from kth order polynomials in additive measures, in the same way… Expand

3 1- PDF

GEOMETRY OF QUANTUM PRINCIPAL BUNDLES II Extended Version

- M. Durdevich
- 1999

A general noncommutative-geometric theory of principal bundles is developed. Quantum groups play the role of structure groups and general quantum spaces play the role of base manifolds. A general… Expand

13 1- PDF

GEOMETRY OF QUANTUM PRINCIPAL BUNDLES III Structure of Calculi and Around

- M. Durdevich
- 2010

We present a general constructive approach to differential calculus on quantum principal bundles. This includes a complete structural analysis of graded differential *-algebras describing horizontal… Expand

9- PDF

Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle

- M. Durdevich, S. B. Sontz
- Mathematics, Physics
- 18 August 2011

A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean spaceE, and then a connection is also defined on this bundle. The covariant derivatives… Expand

13- PDF

Generalized Noiseless Quantum Codes utilizing Quantum Enveloping Algebras

- M. Durdevich, H. Makaruk, R.Owczarek
- Mathematics, Physics
- 28 May 1998

A generalization of the results of Rasetti and Zanardi concerning avoiding errors in quantum computers by using states preserved by evolution is presented. The concept of dynamical symmetry is… Expand

10- PDF

QUANTUM GEOMETRY AND NEW CONCEPT OF SPACE

- M. Durdevich
- 1999

Every geometry deals with some kind of spaces. Quantum geometry deals with quantum spaces, including the classical concept of space as a very special case. In classical geometry spaces are always… Expand

CHARACTERISTIC CLASSES OF QUANTUM PRINCIPAL BUNDLES

- M. Durdevich
- 1999

A noncommutative-geometric generalization of classical Weil theory of characteristic classes is presented, in the conceptual framework of quantum principal bundles. A particular care is given to the… Expand

4- PDF

QUANTUM PRINCIPAL BUNDLES AND CORRESPONDING GAUGE THEORIES

- M. Durdevich
- 1999

A generalization of classical gauge theory is presented, in which compact quantum groups play the role of the internal symmetry groups. All considerations are performed in the framework of a… Expand

5- PDF

QUANTUM PRINCIPAL BUNDLES

- M. Durdevich
- 1999

A noncommutative-geometric generalization of the theory of principal bundles is sketched. A differential calculus over corresponding quantum principal bundles is analyzed. The formalism of… Expand

2- PDF

CLASSICAL SPINOR STRUCTURES ON QUANTUM SPACES

- M. Durdevich
- 1999

A noncommutative-geometric generalization of the classical concept of spinor structure is presented. This is done in the framework of the formalism of quantum principal bundles. In particular,… Expand

3- PDF