Displaying similar documents to “Some remarks on quantum and braided group gauge theory”

A note on coalgebra gauge theory

Tomasz Brzeziński (1997)

Banach Center Publications

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A generalisation of quantum principal bundles in which a quantum structure group is replaced by a coalgebra is proposed.

Quantum Fibre Bundles. An Introduction

Tomasz Brzeziński (1997)

Banach Center Publications

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An approach to construction of a quantum group gauge theory based on the quantum group generalisation of fibre bundles is reviewed.

Quantum classifying spaces and universal quantum characteristic classes

Mićo Đurđević (1997)

Banach Center Publications

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A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced and analyzed. Interrelations with the abstract algebraic theory of quantum characteristic classes are discussed. Various non-equivalent approaches to defining universal characteristic classes are outlined.

Contact Quantization: Quantum Mechanics = Parallel transport

G. Herczeg, E. Latini, Andrew Waldron (2018)

Archivum Mathematicum

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Quantization together with quantum dynamics can be simultaneously formulated as the problem of finding an appropriate flat connection on a Hilbert bundle over a contact manifold. Contact geometry treats time, generalized positions and momenta as points on an underlying phase-spacetime and reduces classical mechanics to contact topology. Contact quantization describes quantum dynamics in terms of parallel transport for a flat connection; the ultimate goal being to also handle quantum...

Quantum principal bundles and their characteristic classes

Mićo Đurđević (1997)

Banach Center Publications

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A general theory of characteristic classes of quantum principal bundles is presented, incorporating basic ideas of classical Weil theory into the conceptual framework of noncommutative differential geometry. A purely cohomological interpretation of the Weil homomorphism is given, together with a geometrical interpretation via quantum invariant polynomials. A natural spectral sequence is described. Some interesting quantum phenomena appearing in the formalism are discussed.