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 B−B- 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