6,657 research outputs found
Commuting Flows and Conservation Laws for Noncommutative Lax Hierarchies
We discuss commuting flows and conservation laws for Lax hierarchies on
noncommutative spaces in the framework of the Sato theory. On commutative
spaces, the Sato theory has revealed essential aspects of the integrability for
wide class of soliton equations which are derived from the Lax hierarchies in
terms of pseudo-differential operators. Noncommutative extension of the Sato
theory has been already studied by the author and Kouichi Toda, and the
existence of various noncommutative Lax hierarchies are guaranteed. In the
present paper, we present conservation laws for the noncommutative Lax
hierarchies with both space-space and space-time noncommutativities and prove
the existence of infinite number of conserved densities. We also give the
explicit representations of them in terms of Lax operators. Our results include
noncommutative versions of KP, KdV, Boussinesq, coupled KdV, Sawada-Kotera,
modified KdV equations and so on.Comment: 22 pages, LaTeX, v2: typos corrected, references added, version to
appear in JM
On localization and position operators in Moebius-covariant theories
Some years ago it was shown that, in some cases, a notion of locality can
arise from the group of symmetry enjoyed by the theory, thus in an intrinsic
way. In particular, when Moebius covariance is present, it is possible to
associate some particular transformations to the Tomita Takesaki modular
operator and conjugation of a specific interval of an abstract circle. In this
context we propose a way to define an operator representing the coordinate
conjugated with the modular transformations. Remarkably this coordinate turns
out to be compatible with the abstract notion of locality. Finally a concrete
example concerning a quantum particle on a line is also given.Comment: 19 pages, UTM 705, version to appear in RM
Coherent states and the quantization of 1+1-dimensional Yang-Mills theory
This paper discusses the canonical quantization of 1+1-dimensional Yang-Mills
theory on a spacetime cylinder, from the point of view of coherent states, or
equivalently, the Segal-Bargmann transform. Before gauge symmetry is imposed,
the coherent states are simply ordinary coherent states labeled by points in an
infinite-dimensional linear phase space. Gauge symmetry is imposed by
projecting the original coherent states onto the gauge-invariant subspace,
using a suitable regularization procedure. We obtain in this way a new family
of "reduced" coherent states labeled by points in the reduced phase space,
which in this case is simply the cotangent bundle of the structure group K.
The main result explained here, obtained originally in a joint work of the
author with B. Driver, is this: The reduced coherent states are precisely those
associated to the generalized Segal-Bargmann transform for K, as introduced by
the author from a different point of view. This result agrees with that of K.
Wren, who uses a different method of implementing the gauge symmetry. The
coherent states also provide a rigorous way of making sense out of the quantum
Hamiltonian for the unreduced system.
Various related issues are discussed, including the complex structure on the
reduced phase space and the question of whether quantization commutes with
reduction
Transition amplitudes and sewing properties for bosons on the Riemann sphere
We consider scalar quantum fields on the sphere, both massive and massless.
In the massive case we show that the correlation functions define amplitudes
which are trace class operators between tensor products of a fixed Hilbert
space. We also establish certain sewing properties between these operators. In
the massless case we consider exponential fields and have a conformal field
theory. In this case the amplitudes are only bilinear forms but still we
establish sewing properties. Our results are obtained in a functional integral
framework.Comment: 33 page
Segal-Bargmann-Fock modules of monogenic functions
In this paper we introduce the classical Segal-Bargmann transform starting
from the basis of Hermite polynomials and extend it to Clifford algebra-valued
functions. Then we apply the results to monogenic functions and prove that the
Segal-Bargmann kernel corresponds to the kernel of the Fourier-Borel transform
for monogenic functionals. This kernel is also the reproducing kernel for the
monogenic Bargmann module.Comment: 11 page
Vertex Operators in 2K Dimensions
A formula is proposed which expresses free fermion fields in 2K dimensions in
terms of the Cartan currents of the free fermion current algebra. This leads,
in an obvious manner, to a vertex operator construction of nonabelian free
fermion current algebras in arbitrary even dimension. It is conjectured that
these ideas may generalize to a wide class of conformal field theories.Comment: Minor change in notation. Change in references
Doppler-free laser spectroscopy of buffer gas cooled molecular radicals
We demonstrate Doppler-free saturated absorption spectroscopy of cold
molecular radicals formed by laser ablation inside a cryogenic buffer gas cell.
By lowering the temperature, congested regions of the spectrum can be
simplified, and by using different temperatures for different regions of the
spectrum a wide range of rotational states can be studied optimally. We use the
technique to study the optical spectrum of YbF radicals with a resolution of 30
MHz, measuring the magnetic hyperfine parameters of the electronic ground
state. The method is suitable for high resolution spectroscopy of a great
variety of molecules at controlled temperature and pressure, and is
particularly well-suited to those that are difficult to produce in the gas
phase.Comment: 11 pages, 4 figure
The Sato Grassmannian and the CH hierarchy
We discuss how the Camassa-Holm hierarchy can be framed within the geometry
of the Sato Grassmannian.Comment: 10 pages, no figure
parafermions from constrained WZNW theories
The conformal field theory based on the coset construction is
treated as the WZNW theory for the affine Lie algebra with the
constrained subalgebra.Using a modification of the generalized
canonical quantization method generators and primary fields of an extended
symmetry algebra are found for arbitrary d.Comment: 14 pages,latex,misprints in formulas 26,40,45 corrected,a reference
adde
Gene-network inference by message passing
The inference of gene-regulatory processes from gene-expression data belongs
to the major challenges of computational systems biology. Here we address the
problem from a statistical-physics perspective and develop a message-passing
algorithm which is able to infer sparse, directed and combinatorial regulatory
mechanisms. Using the replica technique, the algorithmic performance can be
characterized analytically for artificially generated data. The algorithm is
applied to genome-wide expression data of baker's yeast under various
environmental conditions. We find clear cases of combinatorial control, and
enrichment in common functional annotations of regulated genes and their
regulators.Comment: Proc. of International Workshop on Statistical-Mechanical Informatics
2007, Kyot
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