Dual field theory realisations are given for linearised gravity in terms of gauge fields in exotic representations of the Lorentz group. The field equations and dual representations are discussed for a wide class of higher spin gauge fields. For non-linear Einstein gravity, such transformations can be implemented locally in light-cone gauge, or partially implemented in the presence of a Killing...

The principles of special relativity and Einstein’s simple derivation the Lorentz transformation are reviewed. A new is developed in this paper, by a approach light-pulse observation or time-dilation observation. Therefore, under two relativity, there exist equivalent derivations approaches to transformation. emphasizes highlights space while our time. This research reveals, particular way, equ...

Some solutions to the anomalies of ultra high energy cosmic-ray(UHECR) and TeV γ-rays require disturbed non-quadratic dispersion relations, which suggest the Lorentz violation. Also, some new theories such as quantum gravity, string theory and the standard model extension imply the Lorentz violation. In this paper, we derive some transformation laws for the classical parameters of nonlinear fie...

The Lorentz transformation is derived from the simplest thought experiment by using the simplest vector formula from elementary geometry. The result is further used to obtain general velocity and acceleration transformation equations.

We present a classification, up to isomorphisms, of all the homogeneous spaces of the Lorentz group with dimension lower than six. At the same time, we classify, up to conjugation, all the non-discrete closed subgroup of the Lorentz group and all the subalgebras of the Lorentz Lie algebra. We also study the covariant mappings between some pairs of homogeneous spaces. This exercise is done witho...

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...