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Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields

Some remarks about the definition of position operator for relativistic elementary systems

Luciano Fonda, G. C. Ghirardi

Published Aug 1, 1968• 3 citations
Publisher
DOI
10.1007/bf02751619

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Since the important work of Newton and Wigner on the position operator and the localized states, several methods have been developed in the literature to deal with the problem of finding a position operator for relativistic systems. One of the most relevant has been the method based on the use of "canonical" transformations such as the Foldy-Wouthuysen transformation. In this paper, we strictly consider the Foldy-Wouthuysen transformation as a procedure which allows one to write the Bargmann-Wigner equations in a form which in the nonrelativistic limit leads to the Galilei-invariant Schr\"odinger equations for arbitrary spin. As a result of this interpretation, we derive for the position operator and the localized states of elementary systems the same expressions as Newton and Wigner; the spin operator is also obtained. Finally, the Chakrabarti transformation is considered in the same spirit.
Fundamental issues of quantum electrodynamics of nanoelectronic systems essential for further progress of nanotechnology are considered. The zitterbewegung is a hypothetical rapid oscillatory motion of elementary particles (specifically, electrons) that obey relativistic wave equations. Those oscillations (with double rest energy of the fermion) have a place between the positive and negative energy states of the wave packet. Along with other relativistic effects of the quantum field theory (the Lamb shift, the Casimir effect and so on), the zitterbewegung might be a factor making worsen noise characteristics of prospective nanoelectronic devices or limiting possible new constructive solutions in nanotechnology. In defiance of known conclusions of the Copenhagen school, operating with complex wavefunctions, the theory of natural oscillatory systems (TNOS) deals with four-vector analytic-signal wavefunctions having single-side (e.g., nonnegative definite) spectra in the time domain. This allows consider only positive energies for fermions, thus taking away acuteness of the problem until its definitive clarification in experimental way.