We will show how the theory of non-linear realisations can be used to naturally incorporate world line diffeomorphisms and kappa transformations for the point particle and superpoint particle respectively. Similar results also hold for a general p-brane and super p-brane, however, we must in these cases include an additional Lorentz transformation.

We present a definition of time measurement based on high energy photons and the fundamental length scale and show that, for macroscopic time, it is in accord with the Lorentz transformation of special relativity. To do this we define observer in a different way than in special relativity.

Consistency of quantum mechanics in black hole physics requires unusual Lorentz transformation properties of the size and shape of physical systems with momentum beyond the Planck scale. A simple parton model illustrates the kind of behavior which is needed. It is then shown that conventional fundamental string theory shares these features. ⋆ [email protected]

Invariant and covariant forms of the quark-antiquark interaction derived by the method of Eichten and Feinberg are considered. Relations between the various terms imposed by Lorentz transformation constraints, here called Gromes relations, are found to exist in neither case. Details of the Gromes relation proper are reconsidered and inconsistencies found that lead to a violation of covariance.

We obtain transformation equations for the Bell basis states under an arbitrary Lorentz boost and compute the expectation values of the relativistic center of mass spin operator under each of these boosted states. We also obtain expectation values for spin projections along the axes. c © Electronic Journal of Theoretical Physics. All rights reserved.

We study the structure of the phase space of generic models of deformed special relativity which gives rise to a definition of velocity consistent with the deformed Lorentz symmetry. As a byproduct we also determine the laws of transformation of spacetime coordinates.

We re-elaborate on the recent basic result that the action of any multilayer is equivalent to a proper Lorentz transformation. As a consequence, we propose simple optical measurements that can serve as an analogue computer for simulating special relativity. Special attention is paid to the question of the Wigner rotation, showing that it can be easily observed in multilayers.

We study a Hamiltonian realization of the phase space of κ-Poincaré algebra that yields a definition of velocity consistent with the deformed Lorentz symmetry. We are also able to determine the laws of transformation of spacetime coordinates and to define an invariant spacetime metric, and discuss some possible experimental consequences.