Nature appears to be covariant both under the discrete transformation CPT, formed from the product of charge conjugation C, parity inversion P, and time reversal T, and under the continuous Lorentz transformations including rotations and boosts. The CPT theorem links these symmetries, stating that under mild technical assumptions CPT is an exact symmetry of local Lorentzcovariant field theories...

Lorentz Violation is a common feature of Planck-scale phenomenology. We show that the symmetry of Randers spaces deduces a modified dispersion relation, which takes the quantum gravity effects into account. The counterparts of the Lorentz transformation in the Einstein’s Special Relativity are presented explicitly. The coordinate transformations are unitary and form a group. Generators and alge...

A calculus based on pointer-mark coincidences is proposed to define, in a mathematically rigorous way, measurements of space and time intervals. The connection between such measurements in different inertial frames according to the Galilean or Lorentz transformations is then studied using new, simple, and practical clock synchronisation procedures. It is found that measured length intervals are...

In quantum field theory, we actually consider a subgroup of O(1, 3), the proper orthochronous or restricted Lorentz group SO(1, 3) = {Λ ∈ O(1, 3)| detΛ = 1 and Λ0 ≥ 0}, which excludes parity and time-reversal transformations that are thus considered as separate, discrete operations P and T . A generic element Λ of the Lorentz group is given by exponentiating the generators together with the par...

Lorentz transformations of spin density matrices for a particle with positive mass and spin 1/2 are described by maps of the kind used in open quantum dynamics. They show how the Lorentz transformations of the spin depend on the momentum. Since the spin and momentum generally are entangled, the maps generally are not completely positive and act in limited domains. States with two momentum value...

In classical mechanics a procedure for simultaneous synchronization in all inertial frames is consistent with the Galilean transformation. However, if one attempts to achieve such synchronization utilizing light signals , then he will be facing on one hand a break down of absolute simultaneity, and on the other hand, a self-contradictory transformation that has Lorentz transformation, or the co...

The conventional discussion of apparent distortions of space and time in Special Relativity (the Lorentz-Fitzgerald Contraction and Time Dilatation) is extended by considering observations of : (i) moving objects of limited lifetime in their own rest frame ('transient luminous objects') and (ii) a moving extended array of synchro-nised 'equivalent clocks' in a common inertial frame. Application...

In this paper we have studied the nature of kinematical and dynamical laws in κ-Minkowski spacetime from a new perspective: the canonical phase space approach. We have introduced a new form of κ-Minkowski phase space algebra from which we recover the κ-extended finite Lorentz transformations derived in [13]. This is a particular form of a Deformed Special Relativity model that admits a modified...