174 research outputs found
Conserved currents of massless fields of spin s>0
A complete and explicit classification of all locally constructed conserved
currents and underlying conserved tensors is obtained for massless linear
symmetric spinor fields of any spin s>0 in four dimensional flat spacetime.
These results generalize the recent classification in the spin s=1 case of all
conserved currents locally constructed from the electromagnetic spinor field.
The present classification yields spin s>0 analogs of the well-known
electromagnetic stress-energy tensor and Lipkin's zilch tensor, as well as a
spin s>0 analog of a novel chiral tensor found in the spin s=1 case. The chiral
tensor possesses odd parity under a duality symmetry (i.e., a phase rotation)
on the spin s field, in contrast to the even parity of the stress-energy and
zilch tensors. As a main result, it is shown that every locally constructed
conserved current for each s>0 is equivalent to a sum of elementary linear
conserved currents, quadratic conserved currents associated to the
stress-energy, zilch, and chiral tensors, and higher derivative extensions of
these currents in which the spin s field is replaced by its repeated
conformally-weighted Lie derivatives with respect to conformal Killing vectors
of flat spacetime. Moreover, all of the currents have a direct, unified
characterization in terms of Killing spinors. The cases s=2, s=1/2 and s=3/2
provide a complete set of conserved quantities for propagation of gravitons
(i.e., linearized gravity waves), neutrinos and gravitinos, respectively, on
flat spacetime. The physical meaning of the zilch and chiral quantities is
discussed.Comment: 26 pages; final version with minor changes, accepted in Proc. Roy.
Soc. A (London
Parity violating spin-two gauge theories
Nonlinear covariant parity-violating deformations of free spin-two gauge
theory are studied in n>2 spacetime dimensions, using a linearized frame and
spin-connection formalism, for a set of massless spin-two fields. It is shown
that the only such deformations yielding field equations with a second order
quasilinear form are the novel algebra-valued types in n=3 and n=5 dimensions
already found in some recent related work concentrating on lowest order
deformations. The complete form of the deformation to all orders in n=5
dimensions is worked out here and some features of the resulting new
algebra-valued spin-two gauge theory are discussed. In particular, the internal
algebra underlying this theory on 5-dimensional Minkowski space is shown to
cause the energy for the spin-two fields to be of indefinite sign. Finally, a
Kaluza-Klein reduction to n=4 dimensions is derived, giving a parity-violating
nonlinear gauge theory of a coupled set of spin-two, spin-one, and spin-zero
massless fields.Comment: 17 page
Fractional Exact Solutions and Solitons in Gravity
We survay our recent results on fractional gravity theory. It is also
provided the Main Theorem on encoding of geometric data (metrics and
connections in gravity and geometric mechanics) into solitonic hierarchies. Our
approach is based on Caputo fractional derivative and nonlinear connection
formalism.Comment: latex2e, 11pt, 10 pages with table of content; a summary of our talk
at Conference "New Trends in Nanotechnology and Nonlinear Dynamical Systems",
25--27 July, 2010, \c{C}ankaya University, Ankara, Turke
Symplectically-invariant soliton equations from non-stretching geometric curve flows
A moving frame formulation of geometric non-stretching flows of curves in the
Riemannian symmetric spaces and is
used to derive two bi-Hamiltonian hierarchies of symplectically-invariant
soliton equations. As main results, multi-component versions of the sine-Gordon
(SG) equation and the modified Korteweg-de Vries (mKdV) equation exhibiting
invariance are obtained along with their bi-Hamiltonian
integrability structure consisting of a shared hierarchy of symmetries and
conservation laws generated by a hereditary recursion operator. The
corresponding geometric curve flows in and
are shown to be described by a non-stretching wave map and a
mKdV analog of a non-stretching Schr\"odinger map.Comment: 39 pages; remarks added on algebraic aspects of the moving frame used
in the constructio
Hierarchy of Conservation Laws of Diffusion--Convection Equations
We introduce notions of equivalence of conservation laws with respect to Lie
symmetry groups for fixed systems of differential equations and with respect to
equivalence groups or sets of admissible transformations for classes of such
systems. We also revise the notion of linear dependence of conservation laws
and define the notion of local dependence of potentials. To construct
conservation laws, we develop and apply the most direct method which is
effective to use in the case of two independent variables. Admitting
possibility of dependence of conserved vectors on a number of potentials, we
generalize the iteration procedure proposed by Bluman and Doran-Wu for finding
nonlocal (potential) conservation laws. As an example, we completely classify
potential conservation laws (including arbitrary order local ones) of
diffusion--convection equations with respect to the equivalence group and
construct an exhaustive list of locally inequivalent potential systems
corresponding to these equations.Comment: 24 page
Lagrange Anchor for Bargmann-Wigner equations
A Poincare invariant Lagrange anchor is found for the non-Lagrangian
relativistic wave equations of Bargmann and Wigner describing free massless
fields of spin s > 1/2 in four-dimensional Minkowski space. By making use of
this Lagrange anchor, we assign a symmetry to each conservation law.Comment: A contribution to Proceedings of the XXXI Workshop on the Geometric
Methods in Physic
Fractional Analogous Models in Mechanics and Gravity Theories
We briefly review our recent results on the geometry of nonholonomic
manifolds and Lagrange--Finsler spaces and fractional calculus with Caputo
derivatives. Such constructions are used for elaborating analogous models of
fractional gravity and fractional Lagrange mechanics.Comment: latex2e, 11pt, 11 pages with table of content; it is summary of the
results presented in our talk at the 3d Conference on "Nonlinear Science and
Complexity", 28--31 July, 2010, \c{C}hankaya University, Ankara, Turke
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
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