47 research outputs found
A topological mechanism of discretization for the electric charge
We present a topological mechanism of discretization, which gives for the
fundamental electric charge a value equal to the square root of the Planck
constant times the velocity of light, which is about 3.3 times the electron
charge. Its basis is the following recently proved property of the standard
linear classical Maxwell equations: they can be obtained by change of variables
from an underlying topological theory, using two complex scalar fields, the
level curves of which coincide with the magnetic and the electric lines,
respectively.Comment: 10 pages, LaTeX fil
Integrable subsystem of Yang--Mills dilaton theory
With the help of the Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2)
Yang-Mills field, we find an integrable subsystem of SU(2) Yang-Mills theory
coupled to the dilaton. Here integrability means the existence of infinitely
many symmetries and infinitely many conserved currents. Further, we construct
infinitely many static solutions of this integrable subsystem. These solutions
can be identified with certain limiting solutions of the full system, which
have been found previously in the context of numerical investigations of the
Yang-Mills dilaton theory. In addition, we derive a Bogomolny bound for the
integrable subsystem and show that our static solutions are, in fact, Bogomolny
solutions. This explains the linear growth of their energies with the
topological charge, which has been observed previously. Finally, we discuss
some generalisations.Comment: 25 pages, LaTex. Version 3: appendix added where the equivalence of
the field equations for the full model and the submodel is demonstrated;
references and some comments adde
Hopf instantons in Chern-Simons theory
We study an Abelian Chern-Simons and Fermion system in three dimensions. In
the presence of a fixed prescribed background magnetic field we find an
infinite number of fully three-dimensional solutions. These solutions are
related to Hopf maps and are, therefore, labelled by the Hopf index. Further we
discuss the interpretation of the background field.Comment: one minor error corrected, discussion of gauge fixing added, some
references adde
Fermion Zero Modes in Odd Dimensions
We study the zero modes of the Abelian Dirac operator in any odd dimension.
We use the stereographic projection between a dimensional space and a
sphere embedded in a dimensional space. It is shown that the
Dirac operator with a gauge field of uniform field strengths in has
symmetries of SU()U(1) which is a subgroup of SO(). Using group
representation theory, we obtain the number of fermion zero modes, as well as
their explicit forms, in a simple way.Comment: 14 page
Review on possible gravitational anomalies
This is an updated introductory review of 2 possible gravitational anomalies
that has attracted part of the Scientific community: the Allais effect that
occur during solar eclipses, and the Pioneer 10 spacecraft anomaly,
experimented also by Pioneer 11 and Ulysses spacecrafts. It seems that, to
date, no satisfactory conventional explanation exist to these phenomena, and
this suggests that possible new physics will be needed to account for them. The
main purpose of this review is to announce 3 other new measurements that will
be carried on during the 2005 solar eclipses in Panama and Colombia (Apr. 8)
and in Portugal (Oct.15).Comment: Published in 'Journal of Physics: Conferences Series of the American
Institute of Physics'. Contribution for the VI Mexican School on Gravitation
and Mathematical Physics "Approaches to Quantum Gravity" (Playa del Carmen,
Quintana Roo, Mexico, Nov. 21-27, 2004). Updates to this information will be
posted in http://www.lsc-group.phys.uwm.edu/~xavier.amador/anomalies.htm
Complete sets of invariants for dynamical systems that admit a separation of variables
Consider a classical Hamiltonian H in n dimensions consisting of a kinetic energy term plus a potential. If the associated Hamilton–Jacobi equation admits an orthogonal separation of variables, then it is possible to generate algorithmically a canonical basis Q, P where P1 = H, P2, ,Pn are the other second-order constants of the motion associated with the separable coordinates, and {Qi,Qj} = {Pi,Pj} = 0, {Qi,Pj} = ij. The 2n–1 functions Q2, ,Qn,P1, ,Pn form a basis for the invariants. We show how to determine for exactly which spaces and potentials the invariant Qj is a polynomial in the original momenta. We shed light on the general question of exactly when the Hamiltonian admits a constant of the motion that is polynomial in the momenta. For n = 2 we go further and consider all cases where the Hamilton–Jacobi equation admits a second-order constant of the motion, not necessarily associated with orthogonal separable coordinates, or even separable coordinates at all. In each of these cases we construct an additional constant of the motion
Multiple zero modes of the Dirac operator in three dimensions
One of the key properties of Dirac operators is the possibility of a
degeneracy of zero modes. For the Abelian Dirac operator in three dimensions
the construction of multiple zero modes has been sucessfully carried out only
very recently. Here we generalise these results by discussing a much wider
class of Dirac operators together with their zero modes. Further we show that
those Dirac operators that do admit zero modes may be related to Hopf maps,
where the Hopf index is related to the number of zero modes in a simple way.Comment: Latex file, 20 pages, no figure
Superintegrable potentials on 3D Riemannian and Lorentzian spaces with non-constant curvature
A quantum sl(2,R) coalgebra is shown to underly the construction of a large
class of superintegrable potentials on 3D curved spaces, that include the
non-constant curvature analogues of the spherical, hyperbolic and (anti-)de
Sitter spaces. The connection and curvature tensors for these "deformed" spaces
are fully studied by working on two different phase spaces. The former directly
comes from a 3D symplectic realization of the deformed coalgebra, while the
latter is obtained through a map leading to a spherical-type phase space. In
this framework, the non-deformed limit is identified with the flat contraction
leading to the Euclidean and Minkowskian spaces/potentials. The resulting
Hamiltonians always admit, at least, three functionally independent constants
of motion coming from the coalgebra structure. Furthermore, the intrinsic
oscillator and Kepler potentials on such Riemannian and Lorentzian spaces of
non-constant curvature are identified, and several examples of them are
explicitly presented.Comment: 14 pages. Based in the contribution presented at the Group 27
conference, Yerevan, Armenia, August 13-19, 200
Particle creation via relaxing hypermagnetic knots
We demonstrate that particle production for fermions coupled chirally to an
Abelian gauge field like the hypercharge field is provided by the microscopic
mechanism of level crossing. For this purpose we use recent results on zero
modes of Dirac operators for a class of localized hypermagnetic knots.Comment: Latex, 10 pages, no figure