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HIGHER ORDER MEASURES, GENERALIZED QUANTUM MECHANICS AND HOPF ALGEBRAS
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 wayExpand
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GEOMETRY OF QUANTUM PRINCIPAL BUNDLES II Extended Version
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 generalExpand
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GEOMETRY OF QUANTUM PRINCIPAL BUNDLES III Structure of Calculi and Around
We present a general constructive approach to differential calculus on quantum principal bundles. This includes a complete structural analysis of graded differential *-algebras describing horizontalExpand
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Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
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 derivativesExpand
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Generalized Noiseless Quantum Codes utilizing Quantum Enveloping Algebras
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 isExpand
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QUANTUM GEOMETRY AND NEW CONCEPT OF SPACE
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 alwaysExpand
CHARACTERISTIC CLASSES OF QUANTUM PRINCIPAL BUNDLES
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 theExpand
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QUANTUM PRINCIPAL BUNDLES AND CORRESPONDING GAUGE THEORIES
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 aExpand
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QUANTUM PRINCIPAL BUNDLES
A noncommutative-geometric generalization of the theory of principal bundles is sketched. A differential calculus over corresponding quantum principal bundles is analyzed. The formalism ofExpand
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CLASSICAL SPINOR STRUCTURES ON QUANTUM SPACES
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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