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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
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
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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
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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
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
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
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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
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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
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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
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