21,575 research outputs found
Convection displacement current and alternative form of Maxwell-Lorentz equations
Some mathematical inconsistencies in the conventional form of Maxwell's
equations extended by Lorentz for a single charge system are discussed. To
surmount these in framework of Maxwellian theory, a novel convection
displacement current is considered as additional and complementary to the
famous Maxwell displacement current. It is shown that this form of the
Maxwell-Lorentz equations is similar to that proposed by Hertz for
electrodynamics of bodies in motion. Original Maxwell's equations can be
considered as a valid approximation for a continuous and closed (or going to
infinity) conduction current. It is also proved that our novel form of the
Maxwell-Lorentz equations is relativistically invariant. In particular, a
relativistically invariant gauge for quasistatic fields has been found to
replace the non-invariant Coulomb gauge. The new gauge condition contains the
famous relationship between electric and magnetic potentials for one uniformly
moving charge that is usually attributed to the Lorentz transformations. Thus,
for the first time, using the convection displacement current, a physical
interpretation is given to the relationship between the components of the
four-vector of quasistatic potentials. A rigorous application of the new gauge
transformation with the Lorentz gauge transforms the basic field equations into
an independent pair of differential equations responsible for longitudinal and
transverse fields, respectively. The longitudinal components can be interpreted
exclusively from the standpoint of the instantaneous "action at a distance"
concept and leads to necessary conceptual revision of the conventional
Faraday-Maxwell field. The concept of electrodynamic dualism is proposed for
self-consistent classical electrodynamics. It implies simultaneous coexistenceComment: ReVTeX file, 29pp., no figure
Connecting lattice and relativistic models via conformal field theory
We consider the quantum group invariant XXZ-model. In infrared limit it
describes Conformal Field Theory with modified energy-momentum tensor. The
correlation functions are related to solutions of level -4 of qKZ equations. We
describe these solutions relating them to level 0 solutions. We further
consider general matrix elements (form factors) containing local operators and
asymptotic states. We explain that the formulae for solutions of qKZ equations
suggest a decomposition of these matrix elements with respect to states of
corresponding Conformal Field Theory .Comment: 22 pages, 1 figur
Optimized Neural Networks to Search for Higgs Boson Production at the Tevatron
An optimal choice of proper kinematical variables is one of the main steps in
using neural networks (NN) in high energy physics. Our method of the variable
selection is based on the analysis of a structure of Feynman diagrams
(singularities and spin correlations) contributing to the signal and background
processes. An application of this method to the Higgs boson search at the
Tevatron leads to an improvement in the NN efficiency by a factor of 1.5-2 in
comparison to previous NN studies.Comment: 4 pages, 4 figures, partially presented in proceedings of ACAT'02
conferenc
Neutrino production coherence and oscillation experiments
Neutrino oscillations are only observable when the neutrino production,
propagation and detection coherence conditions are satisfied. In this paper we
consider in detail neutrino production coherence, taking \pi\to \mu \nu \ decay
as an example. We compare the oscillation probabilities obtained in two
different ways: (1) coherent summation of the amplitudes of neutrino production
at different points along the trajectory of the parent pion; (2) averaging of
the standard oscillation probability over the neutrino production coordinate in
the source. We demonstrate that the results of these two different approaches
exactly coincide, provided that the parent pion is considered as pointlike and
the detection process is perfectly localized. In this case the standard
averaging of the oscillation probability over the finite spatial extensions of
the neutrino source (and detector) properly takes possible decoherence effects
into account. We analyze the reason for this equivalence of the two approaches
and demonstrate that for pion wave packets of finite width \sigma_{x\pi} the
equivalence is broken. The leading order correction to the oscillation
probability due to \sigma_{x\pi}\ne 0 is shown to be \sim
[v_g/(v_g-v_\pi)]\sigma_{x\pi}/l_{osc}, where v_g and v_\pi \ are the group
velocities of the neutrino and pion wave packets, and l_{osc} is the neutrino
oscillation length.Comment: LaTeX, 40 pages, 4 figures. v2: minor typos correcte
On orthogonal expansions of the space of vector functions which are square-summable over a given domain and the vector analysis operators
The Hilbert space L2(omega) of vector functions is studied. A breakdown of L2(omega) into orthogonal subspaces is discussed and the properties of the operators for projection onto these subspaces are investigated from the standpoint of preserving the differential properties of the vectors being projected. Finally, the properties of the operators are examined
Structure of Matrix Elements in Quantum Toda Chain
We consider the quantum Toda chain using the method of separation of
variables. We show that the matrix elements of operators in the model are
written in terms of finite number of ``deformed Abelian integrals''. The
properties of these integrals are discussed. We explain that these properties
are necessary in order to provide the correct number of independent operators.
The comparison with the classical theory is done.Comment: LaTeX, 17 page
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