2,643 research outputs found
Invariants of genus 2 mutants
Pairs of genus 2 mutant knots can have different Homfly polynomials, for
example some 3-string satellites of Conway mutant pairs. We give examples which
have different Kauffman 3-variable polynomials, answering a question raised by
Dunfield et al in their study of genus 2 mutants. While pairs of genus 2 mutant
knots have the same Jones polynomial, given from the Homfly polynomial by
setting v=s^2, we give examples whose Homfly polynomials differ when v=s^3. We
also give examples which differ in a Vassiliev invariant of degree 7, in
contrast to satellites of Conway mutant knots.Comment: 16 pages, 20 figure
Topologically Massive Gauge Theory: A Lorentzian Solution
We obtain a lorentzian solution for the topologically massive non-abelian
gauge theory on AdS space by means of a SU(1, 1) gauge transformation of the
previously found abelian solution. There exists a natural scale of length which
is determined by the inverse topological mass. The topological mass is
proportional to the square of the gauge coupling constant. In the topologically
massive electrodynamics the field strength locally determines the gauge
potential up to a closed 1-form via the (anti-)self-duality equation. We
introduce a transformation of the gauge potential using the dual field strength
which can be identified with an abelian gauge transformation. Then we present
the map from the AdS space to the pseudo-sphere including the topological mass.
This is the lorentzian analog of the Hopf map. This map yields a global
decomposition of the AdS space as a trivial circle bundle over the upper
portion of the pseudo-sphere which is the Hyperboloid model for the Lobachevski
geometry. This leads to a reduction of the abelian field equation onto the
pseudo-sphere using a global section of the solution on the AdS space. Then we
discuss the integration of the field equation using the Archimedes map from the
pseudo-sphere to the cylinder over the ideal Poincare circle. We also present a
brief discussion of the holonomy of the gauge potential and the dual-field
strength on the upper portion of the pseudo-sphere.Comment: 23 pages, 1 postscript figur
Covariant Hamiltonian Field Theory
A consistent, local coordinate formulation of covariant Hamiltonian field
theory is presented. Whereas the covariant canonical field equations are
equivalent to the Euler-Lagrange field equations, the covariant canonical
transformation theory offers more general means for defining mappings that
preserve the form of the field equations than the usual Lagrangian description.
It is proved that Poisson brackets, Lagrange brackets, and canonical 2-forms
exist that are invariant under canonical transformations of the fields. The
technique to derive transformation rules for the fields from generating
functions is demonstrated by means of various examples. In particular, it is
shown that the infinitesimal canonical transformation furnishes the most
general form of Noether's theorem. We furthermore specify the generating
function of an infinitesimal space-time step that conforms to the field
equations.Comment: 93 pages, no figure
Potential formulation of the dispersion relation for a uniform, magnetized plasma with stationary ions in terms of a vector phasor
The derivation of the helicon dispersion relation for a uniform plasma with
stationary ions subject to a constant background magnetic field is reexamined
in terms of the potential formulation of electrodynamics. Under the same
conditions considered by the standard derivation, the nonlinear self-coupling
between the perturbed electron flow and the potential it generates is
addressed. The plane wave solution for general propagation vector is determined
for all frequencies and expressed in terms of a vector phasor. The behavior of
the solution as described in vacuum units depends upon the ratio of
conductivity to the magnitude of the background field. Only at low conductivity
and below the cyclotron frequency can significant propagation occur as
determined by the ratio of skin depth to wavelength.Comment: 10 pages, 6 figures, major revision, final version, to appear in Po
Comment on "Plasma ionization by annularly bounded helicon waves" [Phys . Plasmas 13, 063501 (2006)]
The neoclassical calculation of the helicon wave theory contains a
fundamental flaw. Use is made of a proportional relationship between the
magnetic field and its curl to derive the Helmholtz equation describing helicon
wave propagation; however, by the fundamental theorem of Stokes, the curl of
the magnetic field must be perpendicular to that portion of the field
contributing to the local curl. Reexamination of the equations of motion
indicates that only electromagnetic waves propagate through a stationary region
of constant pressure in a fully ionized, neutral medium.Comment: 7 pages, 1 figure, to be published in Phys. Plasmas,
http://link.aip.org/link/?PHPAEN/16/054701/
Casimir force in the presence of a magnetodielectric medium
In this article we investigate the Casimir effect in the presence of a medium
by quantizing the Electromagnetic (EM) field in the presence of a
magnetodielectric medium by using the path integral formalism. For a given
medium with definite electric and magnetic susceptibilities, explicit
expressions for the Casimir force are obtained which are in agree with the
original Casimir force between two conducting parallel plates immersed in the
quantum electromagnetic vacuum.Comment: 8 pages, 1 figur
Equivalence between different classical treatments of the O(N) nonlinear sigma model and their functional Schrodinger equations
In this work we derive the Hamiltonian formalism of the O(N) non-linear sigma
model in its original version as a second-class constrained field theory and
then as a first-class constrained field theory. We treat the model as a
second-class constrained field theory by two different methods: the
unconstrained and the Dirac second-class formalisms. We show that the
Hamiltonians for all these versions of the model are equivalent. Then, for a
particular factor-ordering choice, we write the functional Schrodinger equation
for each derived Hamiltonian. We show that they are all identical which
justifies our factor-ordering choice and opens the way for a future
quantization of the model via the functional Schrodinger representation.Comment: Revtex version, 17 pages, substantial change
Massless interacting particles
We show that classical electrodynamics of massless charged particles and the
Yang--Mills theory of massless quarks do not experience rearranging their
initial degrees of freedom into dressed particles and radiation. Massless
particles do not radiate. We consider a version of the direct interparticle
action theory for these systems following the general strategy of Wheeler and
Feynman.Comment: LaTeX; 20 pages; V4: discussion is slightly modified to clarify some
important points, relevant references are adde
A Note on the Relativistic Covariance of the Cyclic Relations
It is shown that the Evans-Vigier modified electrodynamics is compatible with
the Relativity Theory.Comment: ReVTeX file, 14pp., no figure
Quantum gravitational optics: the induced phase
The geometrical approximation of the extended Maxwell equation in curved
spacetime incorporating interactions induced by the vacuum polarization effects
is considered. Taking into account these QED interactions and employing the
analogy between eikonal equation in geometrical optics and Hamilton-Jacobi
equation for the particle motion, we study the phase structure of the modified
theory. There is a complicated, local induced phase which is believed to be
responsible for the modification of the classical picture of light ray. The
main features of QGO could be obtained through the study of this induced phase.
We discuss initial principles in conventional and modified geometrical optics
and compare the results.Comment: 10 pages, REVTex forma
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