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Gauge theories based on quantum groups, representations of the braid group

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dc.contributor Graduate Program in Physics.
dc.contributor.advisor Arık, Metin.
dc.contributor.author Yıldız, Ali.
dc.date.accessioned 2023-03-16T10:38:04Z
dc.date.available 2023-03-16T10:38:04Z
dc.date.issued 1993.
dc.identifier.other PHYS 1993 Y56
dc.identifier.uri http://digitalarchive.boun.edu.tr/handle/123456789/13703
dc.description.abstract Possible formulations of gauge field models where the gauge group is a quantum group are discussed. The exponential map from the generators of the Lie algebra analog of the quantum group SUq(2) to the quantum group SUq(2) itself is presented. The q-deformed Yang-Mills theory is introduced via the definition of the q-trace and the q-deformed YangMills lagrangian which is invariant under the quantum group gauge transformations. The gauge field takes values in the quantum universal enveloping algebra of SUq(2). As a result of this construction a Weinberg type mixing angle which depends on the quantum group deformation parameter q is obtained. The representations of the n-braid group where generators are given essentially by 2 x 2 matrices whose elements belong to a noncommutative algebra are presented. The Burau representation arises as a special (commuting) case of this algebra. A closely related algebra to the braid algebra is introduced and it is shown that the generalized oscillator system given by this algebra generates a hydrogen-like spectrum.
dc.format.extent 30 cm.
dc.publisher Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 1993.
dc.subject.lcsh Gauge fields (Physics)
dc.subject.lcsh Quantum groups.
dc.subject.lcsh Group theory.
dc.title Gauge theories based on quantum groups, representations of the braid group
dc.format.pages vii, 70 leaves;


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