755 research outputs found
Comment on triple gauge boson interactions in the non-commutative electroweak sector
In this comment we present an analysis of electroweak neutral triple gauge
boson couplings projected out of the gauge sector of the extended
non-commutative standard model. A brief overview of the current experimental
situation is given.Comment: 4 page
On Quantum Lie Algebras and Quantum Root Systems
As a natural generalization of ordinary Lie algebras we introduce the concept
of quantum Lie algebras . We define these in terms of certain
adjoint submodules of quantized enveloping algebras endowed with a
quantum Lie bracket given by the quantum adjoint action. The structure
constants of these algebras depend on the quantum deformation parameter and
they go over into the usual Lie algebras when .
The notions of q-conjugation and q-linearity are introduced. q-linear
analogues of the classical antipode and Cartan involution are defined and a
generalised Killing form, q-linear in the first entry and linear in the second,
is obtained. These structures allow the derivation of symmetries between the
structure constants of quantum Lie algebras.
The explicitly worked out examples of and illustrate the
results.Comment: 22 pages, latex, version to appear in J. Phys. A. see
http://www.mth.kcl.ac.uk/~delius/q-lie.html for calculations and further
informatio
The photon-neutrino interaction in non-commutative gauge field theory and astrophysical bounds
In this letter we propose a mechanism of left- and right-handed neutrino couplings to photons, which arises naturally in non-commutative gauge field theory. We estimate the predicted additional energy-loss in stars induced by space-time non-commutativity. The usual requirement that any new energy-loss mechanism in globular cluster stars must not significantly exceed the standard neutrino losses implies a scale of non-commutative gauge theory above the scale of weak interactions
On Quantum Groups in the Hubbard Model with Phonons
The correct Hamiltonian for an extended Hubbard model with quantum group
symmetry as introduced by A. Montorsi and M. Rasetti is derived for a
D-dimensional lattice. It is shown that the superconducting SUq(2) holds as a
true quantum symmetry only for D = 1 and that terms of higher order in the
fermionic operators in addition to phonons are required for a quantum symmetric
hamiltonian. The condition for quantum symmetry is "half filling" and there is
no local electron-phonon coupling. A discussion of Quantum symmetries in
general is given in a formalism that should be readily accessible to non
Hopf-algebraists.Comment: latex, 17 page
Covariant differential complexes on quantum linear groups
We consider the possible covariant external algebra structures for Cartan's
1-forms on GL_q(N) and SL_q(N). We base upon the following natural postulates:
1. the invariant 1-forms realize an adjoint representation of quantum group;
2. all monomials of these forms possess the unique ordering.
For the obtained external algebras we define the exterior derivative
possessing the usual nilpotence condition, and the generally deformed version
of Leibniz rules. The status of the known examples of GL_q(N)-differential
calculi in the proposed classification scheme, and the problems of
SL_q(N)-reduction are discussed.Comment: 23 page
Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
We derive noncommutative Einstein equations for abelian twists and their
solutions in consistently symmetry reduced sectors, corresponding to twisted
FRW cosmology and Schwarzschild black holes. While some of these solutions must
be rejected as models for physical spacetimes because they contradict
observations, we find also solutions that can be made compatible with low
energy phenomenology, while exhibiting strong noncommutativity at very short
distances and early times.Comment: LaTeX 12 pages, JHEP.st
Quantum E(2) groups and Lie bialgebra structures
Lie bialgebra structures on are classified. For two Lie bialgebra
structures which are not coboundaries (i.e. which are not determined by a
classical -matrix) we solve the cocycle condition, find the Lie-Poisson
brackets and obtain quantum group relations. There is one to one correspondence
between Lie bialgebra structures on and possible quantum deformations of
and .Comment: 8 pages, plain TEX, harvmac, to appear in J. Phys.
A Class of Bicovariant Differential Calculi on Hopf Algebras
We introduce a large class of bicovariant differential calculi on any quantum
group , associated to -invariant elements. For example, the deformed
trace element on recovers Woronowicz' calculus. More
generally, we obtain a sequence of differential calculi on each quantum group
, based on the theory of the corresponding braided groups . Here
is any regular solution of the QYBE.Comment: 16 page
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