11,521 research outputs found
Correlation Functions of a Conformal Field Theory in Three Dimensions
We derive explicit forms of the two--point correlation functions of the
non-linear sigma model at the critical point, in the large limit, on
various three dimensional manifolds of constant curvature. The two--point
correlation function, , is the only -point correlation function
which survives in this limit. We analyze the short distance and long distance
behaviour of . It is shown that decays exponentially with
the Riemannian distance on the spaces . The decay on is of course a power law. We
show that the scale for the correlation length is given by the geometry of the
space and therefore the long distance behaviour of the critical correlation
function is not necessarily a power law even though the manifold is of infinite
extent in all directions; this is the case of the hyperbolic space where the
radius of curvature plays the role of a scale parameter. We also verify that
the scalar field in this theory is a primary field with weight ; we illustrate this using the example of the manifold
whose metric is conformally equivalent to that of up to a
reparametrization.Comment: 15 pages, Late
Noncommutative via closed star product
We consider linear star products on of Lie algebra type. First we
derive the closed formula for the polydifferential representation of the
corresponding Lie algebra generators. Using this representation we define the
Weyl star product on the dual of the Lie algebra. Then we construct a gauge
operator relating the Weyl star product with the one which is closed with
respect to some trace functional, . We introduce
the derivative operator on the algebra of the closed star product and show that
the corresponding Leibnitz rule holds true up to a total derivative. As a
particular example we study the space with type
noncommutativity and show that in this case the closed star product is the one
obtained from the Duflo quantization map. As a result a Laplacian can be
defined such that its commutative limit reproduces the ordinary commutative
one. The deformed Leibnitz rule is applied to scalar field theory to derive
conservation laws and the corresponding noncommutative currents.Comment: published versio
Alternative Canonical Formalism for the Wess-Zumino-Witten Model
We study a canonical quantization of the Wess--Zumino--Witten (WZW) model
which depends on two integer parameters rather than one. The usual theory can
be obtained as a contraction, in which our two parameters go to infinity
keeping the difference fixed. The quantum theory is equivalent to a generalized
Thirring model, with left and right handed fermions transforming under
different representations of the symmetry group. We also point out that the
classical WZW model with a compact target space has a canonical formalism in
which the current algebra is an affine Lie algebra of non--compact type.
Also, there are some non--unitary quantizations of the WZW model in which
there is invariance only under half the conformal algebra (one copy of the
Virasoro algebra).Comment: 22 pages; UR-133
On Reduced Time Evolution for Initially Correlated Pure States
A new method to deal with reduced dynamics of open systems by means of the
Schr\"odinger equation is presented. It allows one to consider the reduced time
evolution for correlated and uncorrelated initial conditions.Comment: accepted in Open Sys. Information Dy
Dynamical Aspects of Lie--Poisson Structures
Quantum Groups can be constructed by applying the quantization by deformation
procedure to Lie groups endowed with a suitable Poisson bracket. Here we try to
develop an understanding of these structures by investigating dynamical systems
which are associated with this bracket. We look at and , as
submanifolds of a 4--dimensional phase space with constraints, and deal with
two classes of problems. In the first set of examples we consider some
hamiltonian systems associated with Lie-Poisson structures and we investigate
the equations of the motion. In the second set of examples we consider systems
which preserve the chosen bracket, but are dissipative. However in this
approach, they survive the quantization procedure.Comment: 17 pages, figures not include
From the fuzzy disc to edge currents in Chern-Simons Theory
We present a brief review of the fuzzy disc, the finite algebra approximating
functions on a disc, which we have introduced earlier. We also present a
comparison with recent papers of Balachandran, Gupta and
K\"urk\c{c}\"{u}o\v{g}lu, and of Pinzul and Stern, aimed at the discussion of
edge states of a Chern-Simons theory.Comment: 8 pages, 6 figures, Talk presented at ``Space-time and Fundamental
Interactions: Quantum Aspects'', conference in honour of A. P. Balachandran's
65th birthday. References added and one misprint correcte
2+1 Einstein Gravity as a Deformed Chern-Simons Theory
The usual description of 2+1 dimensional Einstein gravity as a Chern-Simons
(CS) theory is extended to a one parameter family of descriptions of 2+1
Einstein gravity. This is done by replacing the Poincare' gauge group symmetry
by a q-deformed Poincare' gauge group symmetry, with the former recovered when
q-> 1. As a result, we obtain a one parameter family of Hamiltonian
formulations for 2+1 gravity. Although formulated in terms of noncommuting
dreibeins and spin-connection fields, our expression for the action and our
field equations, appropriately ordered, are identical in form to the ordinary
ones. Moreover, starting with a properly defined metric tensor, the usual
metric theory can be built; the Christoffel symbols and space-time curvature
having the usual expressions in terms of the metric tensor, and being
represented by c-numbers. In this article, we also couple the theory to
particle sources, and find that these sources carry exotic angular momentum.
Finally, problems related to the introduction of a cosmological constant are
discussed.Comment: Latex file, 26 pages, no figure
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