Among the symmetries in physics, the rotation symmetry is most familiar to us. It is known that the spherical harmonics serve useful purposes when the world is rotated. Squeeze transformations are also becoming more prominent in physics, particularly in optical sciences and in high-energy physics. As can be seen from Dirac’s light-cone coordinate system, Lorentz boosts are squeeze transformatio...

There is a widespread belief that individual Lorentz–Einstein transformation equations have a physical significance of their own and can be used independently of each other. Thus, for example, some authors believe that for transforming the electric field of a parallel-plate capacitor or of a line charge from one reference frame to another it is sufficient to use only the charge-density transfor...

It was shown by Gribov, Ioffe, Pomeranchuk in 1966 and by Ioffe in 1969 that a space-time picture is needed for the Lorentz deformation of hadronic interaction region. It is shown that this deformation is a squeeze transformation. It is shown also that Feynman's parton picture emerges as a consequence of Lorentz-squeezed hadrons in the quark model.

We study remaining Lorentz symmetry, i.e. Lorentz transformations which leave the noncommutativity parameter θ invariant, within the approach of TOPT to space-time noncommutative theories. Their violation is shown in a simple scattering process. We argue that this results from the non-covariant transformation properties of the phase factors appearing in TOPT. PACS: 11.10.Nx, 11.30.Cp

We study remaining Lorentz symmetry, i.e. Lorentz transformations which leave the noncommutativity parameter θ invariant, within the approach of time-ordered perturbation theory (TOPT) to space-time noncommutative theories. Their violation is shown in a simple scattering process. We argue that this results from the noncovariant transformation properties of the phase factors appearing in TOPT. P...

The parameter changes resulting from a combination of Lorentz transformation are shown to form vector field flows. The exact, finite Thomas rotation angle is determined and interpreted intuitively. Using phase portraits, the parameters evolution can be clearly visualized. In addition to identifying the fixed points, we obtain an analytic invariant, which correlates the evolution of parameters. ...

We show that combining the spatial noncommutative SYM limit and Lorentz transformation, one can obtain a well-behaved light-like noncommutative SYM limit. The light-like noncommutative SYM is unitary. When the boost velocity is finite, the resulting theory with space-time noncommutativity is unitary as well. The light-like noncommutative SYM limit can also be approached by combining the noncomm...

Stokes parameters form a Minkowskian 4-vector under various optical transformations. As a consequence, the resulting two-by-two density matrix constitutes a representation of the Lorentz group. The associated Poincaré sphere is a geometric representation of the Lorentz group. Since the Lorentz group preserves the determinant of the density matrix, it cannot accommodate the decoherence process t...

We reveal the frame-exchange space-inversion (FESI) symmetry and the frame-exchange time-inversion (FETI) symmetry in the Lorentz transformation and propose a symmetry principle stating that the space-time transformation between two inertial frames is invariant under the FESI or the FETI transformation. In combination with the principle of relativity and the presumed nature of Euclidean space a...

Recent work has shown that the underlying assumptions of the Global Positioning System (GPS) are incompatible with a number of conclusions of conventional relativity theory, including Fitzgerald-Lorentz length contraction (FLC) and the supposed ambiguity in the relative rates of clocks in motion. The challenge is therefore to amend relativity theory so as to bring it into full consistency with ...