28,266 research outputs found
Space-time dynamics from algebra representations
We present a model for introducing dynamics into a space-time geometry. This
space-time structure is constructed from a C*-algebra defined in terms of the
generators of an irreducible unitary representation of a finite-dimensional Lie
algebra G. This algebra is included as a subalgebra in a bigger algebra F, the
generators of which mix the representations of G in a way that relates
different space-times and creates the dynamics. This construction can be
considered eventually as a model for 2-D quantum gravity.Comment: 6 pages, LaTeX, no figures. Old paper submitted for archive reason
Non-commutative geometry of 4-dimensional quantum Hall droplet
We develop the description of non-commutative geometry of the 4-dimensional
quantum Hall fluid's theory proposed recently by Zhang and Hu. The
non-commutative structure of fuzzy appears naturally in this theory.
The fuzzy monopole harmonics, which are the essential elements in this
non-commutative geometry, are explicitly constructed and their obeying the
matrix algebra is obtained. This matrix algebra is associative. We also propose
a fusion scheme of the fuzzy monopole harmonics of the coupling system from
those of the subsystems, and determine the fusion rule in such fusion scheme.
By products, we provide some essential ingredients of the theory of SO(5)
angular momentum. In particular, the explicit expression of the coupling
coefficients, in the theory of SO(5) angular momentum, are given. It is
discussed that some possible applications of our results to the 4-dimensional
quantum Hall system and the matrix brane construction in M-theory.Comment: latex 22 pages, no figures. some references added. some results are
clarifie
Quantum Entropy for the Fuzzy Sphere and its Monopoles
Using generalized bosons, we construct the fuzzy sphere and monopoles
on in a reducible representation of . The corresponding quantum
states are naturally obtained using the GNS-construction. We show that there is
an emergent non-abelian unitary gauge symmetry which is in the commutant of the
algebra of observables. The quantum states are necessarily mixed and have
non-vanishing von Neumann entropy, which increases monotonically under a
bistochastic Markov map. The maximum value of the entropy has a simple relation
to the degeneracy of the irreps that constitute the reducible representation
that underlies the fuzzy sphere.Comment: 21 pages, typos correcte
Dirac operator on the q-deformed Fuzzy sphere and Its spectrum
The q-deformed fuzzy sphere is the algebra of
dim. matrices, covariant with respect to the adjoint action
of \uq and in the limit , it reduces to the fuzzy sphere
. We construct the Dirac operator on the q-deformed fuzzy
sphere- using the spinor modules of \uq. We explicitly obtain
the zero modes and also calculate the spectrum for this Dirac operator. Using
this Dirac operator, we construct the \uq invariant action for the spinor
fields on which are regularised and have only finite modes. We
analyse the spectrum for both being root of unity and real, showing
interesting features like its novel degeneracy. We also study various limits of
the parameter space (q, N) and recover the known spectrum in both fuzzy and
commutative sphere.Comment: 19 pages, 6 figures, more references adde
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