Quantum group Gauge theory on quantum spaces
نویسندگان
چکیده
منابع مشابه
Quantum group gauge theory on quantum spaces
We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on SUq(2) . The construction is presented within the setting of a general theory of quantum principal bundles with quantum group (Hopf algebra) fiber, associated quantum vector...
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We study the quantum group gauge theory developed elsewhere in the limit when the base space (spacetime) is a classical space rather than a general quantum space. We show that this limit of the theory for gauge quantum group Uq(g) is isomorphic to usual gauge theory with Lie algebra g. Thus a new kind of gauge theory is not obtained in this way, although we do find some differences in the coupl...
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Gauge theories on q-deformed spaces are constructed using covariant derivatives. For this purpose a “vielbein” is introduced, which transforms under gauge transformations. The non-Abelian case is treated by establishing a connection to gauge theories on commutative spaces, i.e. by a Seiberg-Witten map. As an example we consider the Manin plane. Remarks are made concerning the relation between c...
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We clarify some aspects of quantum group gauge theory and its recent generalisations (by T. Brzezinski and the author) to braided group gauge theory and coalgebra gauge theory. We outline the diagrammatic version of the braided case. We study the bosonisation of any braided group provides as a trivial principal bundle in three ways.
متن کاملGauge Theory on a Quantum Phase Space
In this note we present a operator formulation of gauge theories in a quantum phase space which is specified by a operator algebra. For simplicity we work with the Heisenberg algebra. We introduce the notion of the derivative (transport) and Wilson line (parallel transport) which enables us to construct a gauge theory in a simple way. We illustrate the formulation by a discussion of the Higgs m...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1995
ISSN: 0010-3616,1432-0916
DOI: 10.1007/bf02099359