145 research outputs found
Coadjoint orbits of the Virasoro algebra and the global Liouville equation
The classification of the coadjoint orbits of the Virasoro algebra is
reviewed and is then applied to analyze the so-called global Liouville
equation. The review is self-contained, elementary and is tailor-made for the
application. It is well-known that the Liouville equation for a smooth, real
field under periodic boundary condition is a reduction of the SL(2,R)
WZNW model on the cylinder, where the WZNW field g in SL(2,R) is restricted to
be Gauss decomposable. If one drops this restriction, the Hamiltonian reduction
yields, for the field where is a constant,
what we call the global Liouville equation. Corresponding to the winding number
of the SL(2,R) WZNW model there is a topological invariant in the reduced
theory, given by the number of zeros of Q over a period. By the substitution
, the Liouville theory for a smooth is recovered in
the trivial topological sector. The nontrivial topological sectors can be
viewed as singular sectors of the Liouville theory that contain blowing-up
solutions in terms of . Since the global Liouville equation is
conformally invariant, its solutions can be described by explicitly listing
those solutions for which the stress-energy tensor belongs to a set of
representatives of the Virasoro coadjoint orbits chosen by convention. This
direct method permits to study the `coadjoint orbit content' of the topological
sectors as well as the behaviour of the energy in the sectors. The analysis
confirms that the trivial topological sector contains special orbits with
hyperbolic monodromy and shows that the energy is bounded from below in this
sector only.Comment: Plain TEX, 48 pages, final version to appear in IJMP
Fractional Dirac Bracket and Quantization for Constrained Systems
So far, it is not well known how to deal with dissipative systems. There are
many paths of investigation in the literature and none of them present a
systematic and general procedure to tackle the problem. On the other hand, it
is well known that the fractional formalism is a powerful alternative when
treating dissipative problems. In this paper we propose a detailed way of
attacking the issue using fractional calculus to construct an extension of the
Dirac brackets in order to carry out the quantization of nonconservative
theories through the standard canonical way. We believe that using the extended
Dirac bracket definition it will be possible to analyze more deeply gauge
theories starting with second-class systems.Comment: Revtex 4.1. 9 pages, two-column. Final version to appear in Physical
Review
Onsager-Manning-Oosawa condensation phenomenon and the effect of salt
Making use of results pertaining to Painleve III type equations, we revisit
the celebrated Onsager-Manning-Oosawa condensation phenomenon for charged stiff
linear polymers, in the mean-field approximation with salt. We obtain
analytically the associated critical line charge density, and show that it is
severely affected by finite salt effects, whereas previous results focused on
the no salt limit. In addition, we obtain explicit expressions for the
condensate thickness and the electric potential. The case of asymmetric
electrolytes is also briefly addressed.Comment: to appear in Phys. Rev. Let
Ground state energy of the modified Nambu-Goto string
We calculate, using zeta function regularization method, semiclassical energy
of the Nambu-Goto string supplemented with the boundary, Gauss-Bonnet term in
the action and discuss the tachyonic ground state problem.Comment: 10 pages, LaTeX, 2 figure
Towards a theory of differential constraints of a hydrodynamic hierarchy
We present a theory of compatible differential constraints of a hydrodynamic
hierarchy of infinite-dimensional systems. It provides a convenient point of
view for studying and formulating integrability properties and it reveals some
hidden structures of the theory of integrable systems. Illustrative examples
and new integrable models are exhibited.Comment: Published by JNMP at http://www.sm.luth.se/math/JNMP
Representations of integers by the form x2 + xy + y2 + z2 + zt + t2
Electronic version of an article published in International Journal of Number Theory Volume 04, Issue 05, October 2008, pp. 709-714. DOI: 10.1142/S1793042108001638. Copyright © 2008 World Scientific Publishing Company: http://www.worldscientific.com/worldscinet/ijntWe give an elementary proof of the number of representations of an integer by the quaternary quadratic form x2 + xy + y2 + z2 + zt + t2
Solutions of the Einstein-Dirac and Seiberg-Witten Monopole Equations
We present unique solutions of the Seiberg-Witten Monopole Equations in which
the U(1) curvature is covariantly constant, the monopole Weyl spinor consists
of a single constant component, and the 4-manifold is a product of two Riemann
surfaces of genuses p_1 and p_2. There are p_1 -1 magnetic vortices on one
surface and p_2 - 1 electric ones on the other, with p_1 + p_2 \geq 2 p_1 =
p_2= 1 being excluded). When p_1 = p_2, the electromagnetic fields are
self-dual and one also has a solution of the coupled euclidean
Einstein-Maxwell-Dirac equations, with the monopole condensate serving as
cosmological constant. The metric is decomposable and the electromagnetic
fields are covariantly constant as in the Bertotti-Robinson solution. The
Einstein metric can also be derived from a K\"{a}hler potential satisfying the
Monge-Amp\`{e}re equations.Comment: 22 pages. Rep. no: FGI-99-
Nonsingular solutions of Hitchin's equations for noncompact gauge groups
We consider a general ansatz for solving the 2-dimensional Hitchin's
equations, which arise as dimensional reduction of the 4-dimensional self-dual
Yang-Mills equations, with remarkable integrability properties. We focus on the
case when the gauge group G is given by a real form of SL(2,C). For G=SO(2,1),
the resulting field equations are shown to reduce to either the Liouville,
elliptic sinh-Gordon or elliptic sine-Gordon equations. As opposed to the
compact case, given by G=SU(2), the field equations associated with the
noncompact group SO(2,1) are shown to have smooth real solutions with
nonsingular action densities, which are furthermore localized in some sense. We
conclude by discussing some particular solutions, defined on R^2, S^2 and T^2,
that come out of this ansatz.Comment: 12 pages, 3 figures. To appear in Nonlinearit
Differential constraints for the Kaup -- Broer system as a reduction of the 1D Toda lattice
It is shown that some special reduction of infinite 1D Toda lattice gives
differential constraints compatible with the Kaup -- Broer system. A family of
the travelling wave solutions of the Kaup -- Broer system and its higher
version is constructed.Comment: LaTeX, uses IOP styl
Nonrelativistic Chern-Simons Vortices on the Torus
A classification of all periodic self-dual static vortex solutions of the
Jackiw-Pi model is given. Physically acceptable solutions of the Liouville
equation are related to a class of functions which we term
Omega-quasi-elliptic. This class includes, in particular, the elliptic
functions and also contains a function previously investigated by Olesen. Some
examples of solutions are studied numerically and we point out a peculiar
phenomenon of lost vortex charge in the limit where the period lengths tend to
infinity, that is, in the planar limit.Comment: 25 pages, 2+3 figures; improved exposition, corrected typos, added
one referenc
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