904 research outputs found
Coalgebra Gauge Theory
We develop a generalised gauge theory in which the role of gauge group is
played by a coalgebra and the role of principal bundle by an algebra. The
theory provides a unifying point of view which includes quantum group gauge
theory, embeddable quantum homogeneous spaces and braided group gauge theory,
the latter being introduced now by these means. Examples include ones in which
the gauge groups are the braided line and the quantum plane.Comment: 32 pages, LaTeX, uses eps
Quantum Particle on a Quantum Circle
We describe a -deformed dynamical system corresponding to the quantum free
particle moving along the circle. The algebra of observables is constructed and
discussed. We construct and classify irreducible representations of the system.Comment: 11 pages, LaTe
q-deformed Dirac Monopole With Arbitrary Charge
We construct the deformed Dirac monopole on the quantum sphere for arbitrary
charge using two different methods and show that it is a quantum principal
bundle in the sense of Brzezinski and Majid. We also give a connection and
calculate the analog of its Chern number by integrating the curvature over
.Comment: Technical modifications made on the definition of the base. A more
geometrical trivialization is used in section
Lattice Gauge Theory
We reformulate the Hamiltonian approach to lattice gauge theories such that,
at the classical level, the gauge group does not act canonically, but instead
as a Poisson-Lie group. At the quantum level, it then gets promoted to a
quantum group gauge symmetry. The theory depends on two parameters - the
deformation parameter and the lattice spacing . We show that the
system of Kogut and Susskind is recovered when , while
QCD is recovered in the continuum limit (for any ). We thus have the
possibility of having a two parameter regularization of QCD.Comment: 26 pages, LATEX fil
Z-graded differential geometry of quantum plane
In this work, the Z-graded differential geometry of the quantum plane is
constructed. The corresponding quantum Lie algebra and its Hopf algebra
structure are obtained. The dual algebra, i.e. universal enveloping algebra of
the quantum plane is explicitly constructed and an isomorphism between the
quantum Lie algebra and the dual algebra is given.Comment: 17 page
Metric On Quantum Spaes
We introduce the analogue of the metric tensor in case of -deformed
differential calculus. We analyse the consequences of the existence of such
metric, showing that this enforces severe restrictions on the parameters of the
theory. We discuss in detail the examples of the Manin plane and the
-deformation of . Finally we touch the topic of relations with the
Connes' approach.Comment: 7 pages (LaTeX), preprint TPJU 14/9
A square root of the harmonic oscillator
Allowing for the inclusion of the parity operator, it is possible to
construct an oscillator model whose Hamiltonian admits an EXACT square root,
which is different from the conventional approach based on creation and
annihilation operators. We outline such a model, the method of solution and
some generalizations.Comment: RevTex, 10 pages in preprint form, no figure
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