158 research outputs found
From Superluminal Velocity To Time Machines?
Various experiments have shown superluminal group and signal velocities
recently. Experiments were essentials carried out with microwave tunnelling,
with frustrated total internal reflection, and with gain-assisted anomalous
dispersion. According to text books a superluminal signal velocity violates
Einstein causality implying that cause and effect can be changed and time
machines known from science fiction could be constructed. This naive analysis,
however, assumes a signal to be a point in the time dimension neglecting its
finite duration. A signal is not presented by a point nor by its front, but by
its total length. On the other hand a signal energy is finite thus its
frequency band is limited, the latter is a fundamental physical property in
consequence of field quantization with quantum . All superluminal
experiments have been carried out with rather narrow frequency bands. The
narrow band width is a condition sine qua non to avoid pulse reshaping of the
signal due to the dispersion relation of the tunnelling barrier or of the
excited gas, respectively. In consequence of the narrow frequency band width
the time duration of the signal is long so that causality is preserved.
However, superluminal signal velocity shortens the otherwise luminal time span
between cause and effect.Comment: 5 pages, 3 figure
Two-Loop Ultrasoft Running of the O(v^2) QCD Quark Potentials
The two-loop ultrasoft contributions to the next-to-leading logarithmic (NLL)
running of the QCD potentials at order v^2 are determined. The results
represent an important step towards the next-to-next-to-leading logarithmic
(NNLL) description of heavy quark pair production and annihilation close to
threshold.Comment: 13 pages, 3 figures; typos corrected, reference added, information on
cross checks added on page 7; acknowledgments adde
Teaching the hidden symmetry of the Kepler problem in relativistic quantum mechanics - from Pauli to Dirac electron
Hidden symmetry in Coulomb interaction is one of the mysterious problems of
modern physics. Additional conserved quantities associated with extra symmetry
govern wide variety of physics problems, from planetary motion till fine and
hyperfine structures of atomic spectra. In this paper we present a simple
derivation of hidden symmetry operator in relativistic quantum mechanics for
the Dirac equation in the Coulomb field. We established that this operator may
be reduced to the one introduced by Johnson and Lippmann. It is worthwhile to
notice that this operator was discussed in literature very rarely and so is not
known well among physicists and was omitted even in the recent textbooks on
relativistic quantum mechanics and/or quantum electrodynamics.Comment: 5 page
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