Clebsch (String) Parameterization of 3-Vectors and Their Actions

We discuss some properties of the intrinsically nonlinear Clebsch decomposition of a vector field into three scalars in d=3. In particular, we note and account for the incompleteness of this parameterization when attempting to use it in variational principles involving Maxwell and Chern-Simons actions. Similarities with string decomposition of metrics and their actions are also pointed out.Comment: 4 pages, LaTeX; email correspondence to [email protected]

Creation and evolution of magnetic helicity

Projecting a non-Abelian SU(2) vacuum gauge field - a pure gauge constructed from the group element U - onto a fixed (electromagnetic) direction in isospace gives rise to a nontrivial magnetic field, with nonvanishing magnetic helicity, which coincides with the winding number of U. Although the helicity is not conserved under Maxwell (vacuum) evolution, it retains one-half its initial value at infinite time.Comment: Clarifying remarks and references added; 12 pages, 1 figure using BoxedEPSF, REVTeX macros; submitted to Phys Rev D; email to [email protected]

Chern-Simons Reduction and non-Abelian Fluid Mechanics

We propose a non-Abelian generalization of the Clebsch parameterization for a vector in three dimensions. The construction is based on a group-theoretical reduction of the Chern-Simons form on a symmetric space. The formalism is then used to give a canonical (symplectic) discussion of non-Abelian fluid mechanics, analogous to the way the Abelian Clebsch parameterization allows a canonical description of conventional fluid mechanics.Comment: 12 pages, REVTeX; revised for publication in Phys Rev D; email to [email protected]

Conservation laws of scaling-invariant field equations

A simple conservation law formula for field equations with a scaling symmetry is presented. The formula uses adjoint-symmetries of the given field equation and directly generates all local conservation laws for any conserved quantities having non-zero scaling weight. Applications to several soliton equations, fluid flow and nonlinear wave equations, Yang-Mills equations and the Einstein gravitational field equations are considered.Comment: 18 pages, published version in J. Phys. A:Math. and Gen. (2003). Added discussion of vorticity conservation laws for fluid flow; corrected recursion formula and operator for vector mKdV conservation law

A model of glueballs

We model the observed glueball mass spectrum in terms of energies for tightly knotted and linked QCD flux tubes. The data is fit well with one parameter. We predict additional glueball masses.Comment: 11 pages, 3 figures, 1 table; minor changes, comments added, typos correcte

Signatures of large-scale magnetic fields in AGN jets: transverse asymmetries

We investigate the emission properties that a large-scale helical magnetic field imprints on AGN jet synchrotron radiation. A cylindrically symmetric relativistic jet and large-scale helical magnetic field produce significant asymmetrical features in transverse profiles of fractional linear polarization, intensity, Faraday rotation, and spectral index. The asymmetrical features of these transverse profiles correlate with one another in ways specified by the handedness of the helical field, the jet viewing angle (theta_ob), and the bulk Lorentz factor of the flow (Gamma). Thus, these correlations may be used to determine the structure of the magnetic field in the jet. In the case of radio galaxies (theta_ob~1 radian) and a subclass of blazars with particularly small viewing angles (theta_ob << 1/Gamma), we find an edge-brightened intensity profile that is similar to that observed in the radio galaxy M87. We present observations of the AGNs 3C 78 and NRAO 140 that display the type of transverse asymmetries that may be produced by large-scale helical magnetic fields.Comment: accepted by MNRAS, added reference

Perfect Fluid Theory and its Extensions

We review the canonical theory for perfect fluids, in Eulerian and Lagrangian formulations. The theory is related to a description of extended structures in higher dimensions. Internal symmetry and supersymmetry degrees of freedom are incorporated. Additional miscellaneous subjects that are covered include physical topics concerning quantization, as well as mathematical issues of volume preserving diffeomorphisms and representations of Chern-Simons terms (= vortex or magnetic helicity).Comment: 3 figure

Knotty inflation and the dimensionality of spacetime

We suggest a structure for the vacuum comprised of a network of tightly knotted/linked flux tubes formed in a QCD-like cosmological phase transition and show that such a network can drive cosmological inflation. As the network can be topologically stable only in three space dimensions, this scenario provides a dynamical explanation for the existence of exactly three large spatial dimensions in our Universe