21 research outputs found
Decomposing the Yang-Mills Field
Recently we have proposed a set of variables for describing the physical
parameters of SU(N) Yang--Mills field. Here we propose an off-shell
generalization of our Ansatz. For this we envoke the Darboux theorem to
decompose arbitrary one-form with respect to some basis of one-forms. After a
partial gauge fixing we identify these forms with the preimages of holomorphic
and antiholomorphic forms on the coset space , identified as
a particular coadjoint orbit. This yields an off-shell gauge fixed
decomposition of the Yang-Mills connection that contains our original variables
in a natural fashion.Comment: 5 pages, latex, no figure
Aspects of Electric and Magnetic Variables in SU(2) Yang-Mills Theory
We introduce a novel decomposition of the four dimensional SU(2) gauge field.
This decomposition realizes explicitely a symmetry between electric and
magnetic variables, suggesting a duality picture between the corresponding
phases. It also indicates that at large distances the Yang-Mills theory
involves a three component unit vector field, a massive Lorentz vector field,
and a neutral scalar field that condenses which yields the mass scale. Our
results are consistent with the proposal that the physical spectrum of the
theory contains confining strings which are tied into stable knotted solitons.Comment: we have made substantial improvement
Spin-Charge Separation, Conformal Covariance and the SU(2) Yang-Mills Theory
In the low energy domain of four-dimensional SU(2) Yang-Mills theory the spin
and the charge of the gauge field can become separated from each other. The
ensuing field variables describe the interacting dynamics between a version of
the O(3) nonlinear -model and a nonlinear Grassmannian -model,
both of which may support closed knotted strings as stable solitons. Lorentz
transformations act projectively in the O(3) model which breaks global internal
rotation symmetry and removes massless Goldstone bosons from the particle
spectrum. The entire Yang-Mills Lagrangian can be recast into a generally
covariant form with a conformally flat metric tensor. The result contains the
Einstein-Hilbert Lagrangian together with a nonvanishing cosmological constant,
and insinuates the presence of a novel dimensionfull parameter in the
Yang-Mills theory.Comment: some misprints in equations correcte
CONNECTIONS of the LIOUVILLE MODEL and XXZ SPIN CHAIN
The quantum theory of the Liouville model with imaginary field is considered
using the quantum inverse scattering method. An integrable structure with
nontrivial spectral parameter dependence is developed for lattice Liouville
theory by scaling the -matrix of lattice sine-Gordon theory. This -matrix
yields Bethe Ansatz equations for Liouville theory, by the methods of the
algebraic Bethe Ansatz. Using the string picture of exited Bethe states, the
lattice Liouville Bethe equations are mapped to the corresponding equations for
the spin 1/2 XXZ chain. The well developed theory of finite size corrections in
spin chains is used to deduce the conformal properties of the lattice Liouville
Bethe states. The unitary series of conformal field theories emerge for
Liouville couplings of the form \gam = \pi\frac{\nu}{\nu+1}, corresponding to
root of unity XXZ anisotropies. The Bethe states give the full spectrum of the
corresponding unitary conformal field theory, with the primary states in the
\Kac table parameterized by a string length , and the remnant of the chain
length mod .Comment: 25 pages, Late
Shafranov's virial theorem and magnetic plasma confinement
Shafranov's virial theorem implies that nontrivial magnetohydrodynamical
equilibrium configurations must be supported by externally supplied currents.
Here we extend the virial theorem to field theory, where it relates to
Derrick's scaling argument on soliton stability. We then employ virial
arguments to investigate a realistic field theory model of a two-component
plasma, and conclude that stable localized solitons can exist in the bulk of a
finite density plasma. These solitons entail a nontrivial electric field which
implies that purely magnetohydrodynamical arguments are insufficient for
describing stable, nontrivial structures within the bulk of a plasma.Comment: 9 pages no figure
Partially Dual variables in SU(2) Yang-Mills Theory
We propose a reformulation of SU(2) Yang-Mills theory in terms of new
variables. These variables are appropriate for describing the theory in its
infrared limit, and indicate that it admits knotlike configurations as stable
solitons. As a consequence we arrive at a dual picture of the Yang-Mills theory
where the short distance limit describes asymptotically free, massless point
gluons and the large distance limit describes extended, massive knotlike
solitons.Comment: 4 pages, revtex twocolum
Hidden symmetry and knot solitons in a charged two-condensate Bose system
We show that a charged two-condensate Ginzburg-Landau model or equivalently a
Gross-Pitaevskii functional for two charged Bose condensates, can be mapped
onto a version of the nonlinear O(3) -model. This implies in particular
that such a system possesses a hidden O(3) symmetry and allows for the
formation of stable knotted solitons. The results, in particular, should be
relevant to the superconducting MgB_2.Comment: This version will appear in Phys. Rev. B, added a comment on the case
when condensates in two bands do not independently conserve, also added a
figure and references to experimental papers on MgB_2 (for which our study is
relevant). Miscellaneous links on knot solitons are also available at the
homepage of one of the authors http://www.teorfys.uu.se/PEOPLE/egor/ .
Animations of knot solitons are available at
http://users.utu.fi/h/hietarin/knots/c45_p2.mp