830 research outputs found
Conformal covariance of massless free nets
In the present paper we review in a fibre bundle context the covariant and
massless canonical representations of the Poincare' group as well as certain
unitary representations of the conformal group (in 4 dimensions). We give a
simplified proof of the well-known fact that massless canonical representations
with discrete helicity extend to unitary and irreducible representations of the
conformal group mentioned before. Further we give a simple new proof that
massless free nets for any helicity value are covariant under the conformal
group. Free nets are the result of a direct (i.e. independent of any explicit
use of quantum fields) and natural way of constructing nets of abstract
C*-algebras indexed by open and bounded regions in Minkowski space that satisfy
standard axioms of local quantum physics. We also give a group theoretical
interpretation of the embedding {\got I} that completely characterizes the
free net: it reduces the (algebraically) reducible covariant representation in
terms of the unitary canonical ones. Finally, as a consequence of the conformal
covariance we also mention for these models some of the expected algebraic
properties that are a direct consequence of the conformal covariance (essential
duality, PCT--symmetry etc.).Comment: 31 pages, Latex2
Helicity supersymmetry of dyons
The 'dyon' system of D'Hoker and Vinet consisting of a spin 1/2 particle with
anomalous gyromagnetic ratio 4 in the combined field of a Dirac monopole plus a
Coulomb plus a suitable potential (which arises in the long-range limit
of a self-dual monopole) is studied following Biedenharn's approach to the
Dirac-Coulomb problem: the explicit solution is obtained using the
`Biedenharn-Temple operator', , and the extra two-fold degeneracy is
explained by the subtle supersymmetry generated by the 'Dyon Helicity' or
generalized `Biedenharn-Johnson-Lippmann' operator . The new SUSY
anticommutes with the chiral SUSY discussed previously.Comment: 14 pages, 2 figure
Superluminal X-shaped beams propagating without distortion along a coaxial guide
In a previous paper [Phys. Rev. E64 (2001) 066603; e-print physics/0001039],
we showed that localized Superluminal solutions to the Maxwell equations exist,
which propagate down (non-evanescence) regions of a metallic cylindrical
waveguide. In this paper we construct analogous non-dispersive waves
propagating along coaxial cables. Such new solutions, in general, consist in
trains of (undistorted) Superluminal "X-shaped" pulses. Particular attention is
paid to the construction of finite total energy solutions. Any results of this
kind may find application in the other fields in which an essential role is
played by a wave-equation (like acoustics, geophysics, etc.). [PACS nos.:
03.50.De; 41.20;Jb; 83.50.Vr; 62.30.+d; 43.60.+d; 91.30.Fn; 04.30.Nk; 42.25.Bs;
46.40.Cd; 52.35.Lv. Keywords: Wave equations; Wave propagation; Localized
beams; Superluminal waves; Coaxial cables; Bidirectional decomposition; Bessel
beams; X-shaped waves; Maxwell equations; Microwaves; Optics; Special
relativity; Coaxial metallic waveguides; Acoustics; Seismology; Mechanical
waves; Elastic waves; Guided gravitational waves.]Comment: plain LaTeX file (22 pages), plus 15 figures; in press in Phys. Rev.
Extended MacMahon-Schwinger's Master Theorem and Conformal Wavelets in Complex Minkowski Space
We construct the Continuous Wavelet Transform (CWT) on the homogeneous space
(Cartan domain) D_4=SO(4,2)/(SO(4)\times SO(2)) of the conformal group SO(4,2)
(locally isomorphic to SU(2,2)) in 1+3 dimensions. The manifold D_4 can be
mapped one-to-one onto the future tube domain C^4_+ of the complex Minkowski
space through a Cayley transformation, where other kind of (electromagnetic)
wavelets have already been proposed in the literature. We study the unitary
irreducible representations of the conformal group on the Hilbert spaces
L^2_h(D_4,d\nu_\lambda) and L^2_h(C^4_+,d\tilde\nu_\lambda) of square
integrable holomorphic functions with scale dimension \lambda and continuous
mass spectrum, prove the isomorphism (equivariance) between both Hilbert
spaces, admissibility and tight-frame conditions, provide reconstruction
formulas and orthonormal basis of homogeneous polynomials and discuss symmetry
properties and the Euclidean limit of the proposed conformal wavelets. For that
purpose, we firstly state and prove a \lambda-extension of Schwinger's Master
Theorem (SMT), which turns out to be a useful mathematical tool for us,
particularly as a generating function for the unitary-representation functions
of the conformal group and for the derivation of the reproducing (Bergman)
kernel of L^2_h(D_4,d\nu_\lambda). SMT is related to MacMahon's Master Theorem
(MMT) and an extension of both in terms of Louck's SU(N) solid harmonics is
also provided for completeness. Convergence conditions are also studied.Comment: LaTeX, 40 pages, three new Sections and six new references added. To
appear in ACH
Detecting Neutrino Magnetic Moments with Conducting Loops
It is well established that neutrinos have mass, yet it is very difficult to
measure those masses directly. Within the standard model of particle physics,
neutrinos will have an intrinsic magnetic moment proportional to their mass. We
examine the possibility of detecting the magnetic moment using a conducting
loop. According to Faraday's Law of Induction, a magnetic dipole passing
through a conducting loop induces an electromotive force, or EMF, in the loop.
We compute this EMF for neutrinos in several cases, based on a fully covariant
formulation of the problem. We discuss prospects for a real experiment, as well
as the possibility to test the relativistic formulation of intrinsic magnetic
moments.Comment: 6 pages, 4 b/w figures, uses RevTe
Klauder's coherent states for the radial Coulomb problem in a uniformly curved space and their flat-space limits
First a set of coherent states a la Klauder is formally constructed for the
Coulomb problem in a curved space of constant curvature. Then the flat-space
limit is taken to reduce the set for the radial Coulomb problem to a set of
hydrogen atom coherent states corresponding to both the discrete and the
continuous portions of the spectrum for a fixed \ell sector.Comment: 10 pages, no figure
Operator Transformations Between Exactly Solvable Potentials and Their Lie Group Generators
One may obtain, using operator transformations, algebraic relations between
the Fourier transforms of the causal propagators of different exactly solvable
potentials. These relations are derived for the shape invariant potentials.
Also, potentials related by real transformation functions are shown to have the
same spectrum generating algebra with Hermitian generators related by this
operator transformation.Comment: 13 pages with one Postscript figure, uses LaTeX2e with revte
From the Mendeleev periodic table to particle physics and back to the periodic table
We briefly describe in this paper the passage from Mendeleev's chemistry
(1869) to atomic physics (in the 1900's), nuclear physics (in the 1932's) and
particle physics (from 1953 to 2006). We show how the consideration of
symmetries, largely used in physics since the end of the 1920's, gave rise to a
new format of the periodic table in the 1970's. More specifically, this paper
is concerned with the application of the group SO(4,2)xSU(2) to the periodic
table of chemical elements. It is shown how the Madelung rule of the atomic
shell model can be used for setting up a periodic table that can be further
rationalized via the group SO(4,2)xSU(2) and some of its subgroups. Qualitative
results are obtained from this nonstandard table.Comment: 15 pages; accepted for publication in Foundations of Chemistry
(special issue to commemorate the one hundredth anniversary of the death of
Mendeleev who died in 1907); version 2: 16 pages; some sentences added;
acknowledgment and references added; misprints correcte
Unified description of 0+ states in a large class of nuclear collective models
A remarkably simple regularity in the energies of 0+ states in a broad class
of collective models is discussed. A single formula for all 0+ states in
flat-bottomed infinite potentials that depends only on the number of dimensions
and a simpler expression applicable to all three IBA symmetries in the large
boson number limit are presented. Finally, a connection between the energy
expression for 0+ states given by the X(5) model and the predictions of the IBA
near the critical point is explored.Comment: 4 pages, 3 postscript figures, uses revTe
Conformally related massless fields in dS, AdS and Minkowski spaces
In this paper we write down the equation for a scalar conformally coupled
field simultaneously for de Sitter (dS), anti-de Sitter (AdS) and Minkowski
spacetime in d-dimensions. The curvature dependence appears in a very simple
way through a conformal factor. As a consequence the process of curvature free
limit, including wave functions limit and two-points functions, turns to be a
straightforward issue. We determine a set of modes, that we call de Sitter
plane waves, which become ordinary plane waves when the curvature vanishes.Comment: 7 pages, 1 figur
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