Article

# On the existence of undistorted progressive waves (UPWs) of arbitrary speeds 0≤ϑ

Foundations of Physics (Impact Factor: 1.17). 27(3):435-508. DOI: 10.1007/BF02550165

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**ABSTRACT:**The aim of this short communication is to report that Gegenbauer's (partial-wave) expansion, that may be used (under some specific conditions) to represent the incident field of an acoustical (or optical) high-order Bessel beam (HOBB) in spherical coordinates, anticipates earlier expressions for undistorted waves. The incident wave-field is written in terms of the spherical Bessel function of the first kind, the gamma function as well as the Gegenbauer or ultraspherical functions given in terms of the associated Legendre functions when the order m of the HOBB is an integer number. Expressions for high-order and zero-order Bessel beams as well as for plane progressive waves reported in prior works can be deduced from Gegenbauer's partial-wave expansion by appropriate choice of the beams' parameters. Hence the value of this note becomes historical. In addition, Gegenbauer's expansion in spherical coordinates may be used to advantage to model the wave-field of a fractional HOBB at the origin (i.e. z=0).Ultrasonics 02/2010; 50(6):541-3. · 2.03 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We examine the effect of superluminal signal propagation through a birefringent crystal, where the effect is not due to absorption or reflection, but to the filtration of a special polarization component. We first examine the effect by a stationary phase analysis, with results consistent with those of an earlier analysis of the system. We supplement this analysis by considering the transit of a gaussian wave and find bounds for the validity of the stationary phase result. The propagation of the gaussian wave is illustrated by figures.11/2007; - [Show abstract] [Hide abstract]

**ABSTRACT:**By analyzing the structure of the Weyl spinor field in the Clifford bundle formalism we show that in each spinorial frame it is represented by F\insec(\doublebarwedge^0 T^\starM + \doublebarwedge^2 T^\star M + \doublebarwedge^{4} T^\star M)\hookrightarrowsecC\ell(M,g) satisfying the equation \partialF=0, where \partial is the Dirac operator acting on sections of the Clifford bundle C\ell(M,g). With this result we show that introducing a generalized potential A=(A + \gamma_5 B)\insec(\doublebarwedge^{1}T^{\star}M + \doublebarwedge^3 T^\star M)\hookrightarrowsecC\ell(M,g) for the Weyl field such that F=\partialA it is possible to exhibit superluminal solutions (including one with a front moving at superluminal speed) for Weyl equation, which surprisingly describes the propagation of a massive tachyonic neutrino. We propose to interpret these extraordinary solutions in order that eventually they may serve as possible models for the emission process and propagation of the superluminal neutrinos observed at the OPERA experiment. Moreover, complementing this study we show that general local chiral invariance of Weyl equation implies that it describes for all solutions that are eigenstates of the parity operator a pair of `sub-particles' carrying opposite magnetic charges (thus possibly carrying a small magnetic moment) which thus interact with an external electromagnetic field. Even if at the Earth's electromagnetic field the effect may result negligible, eventually the idea may be a useful one to study neutrinos leaving the electromagnetic field of stars.10/2011;

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