Abstract:
We develop a geometrical framework that allows to obtain the electromagnetic field quantities in accelerated frames. The frame of arbitrary accelerated observers in space-time is defined by a suitable set of tetrad fields, whose timelike components are adapted to the worldlines of a field of observers. We consider the Faraday tensor and Maxwell's equations as abstract tensor quantities in space-time, and make use of tetrad fields to project the electromagnetic field quantities in the accelerated frames. As an application, plane and spherical electromagnetic waves are projected in linearly accelerated frames in Minkowski space-time. We show that the amplitude, frequency and the wave vector of the plane wave in the accelerated frame vary with time, while the light speed remains constant. We also obtain the variation of the Poynting vector with time in the accelerated frame.

Abstract:
The electrodynamics both in RF with prescribed law of motion and in FR with prescribed structure is considered. Parallel comparison for solutions in “uniformly accelerated” NRF M?ller system and in uniformly accelerated rigid NFR in the space of the constant curvature is carried out. The stationary criterion is formulated. On the basis of this criterion, one of the “eternal physical problems” concerning the field at uniformly accelerated charge motion is considered. The problems of electromagnetic wave spreading, Doppler’s effect and field transformations are discussed.

Abstract:
Quantized fields in accelerated frames (Rindler spaces) with emphasis on gauge fields are investigated. Important properties of the dynamics in Rindler spaces are shown to follow from the scale invariance of the corresponding Hamiltonians. Origin and consequences of this extraordinary property of Hamiltonians in Rindler spaces are elucidated. Characteristics of the Unruh radiation, the appearance of a photon condensate and the interaction energy of vector and scalar static charges are discussed and implications for Yang-Mills theories and QCD in Rindler spaces are indicated.

Abstract:
The geometrical and quantum mechanical basis for Davies' and Unruh's acceleration temperature is traced to a type of quantum mechanical (``achronal'') spin. Its existence and definition are based on pairs of causally disjoint accelerated frames. For bosons the expected spin vector of monochromatic particles is given by the ``Planckian power'' and the ``r.m.s. thermal fluctuation'' spectra. Under spacetime translation the spin direction precesses around that ``Planckian'' vector. By exhibiting the conserved achronal spin four-current, we extend the identification of achronal spin from single quanta to multiparticle systems. Total achronal spin conservation is also shown to hold, even in the presence of quadratic interactions.

Abstract:
In this article, Generalized Principle of "limiting 4-dimensional symmetry": The laws of physics in non-inertial frames must display the 4-dimensional symmetry of the Generalized Lorentz-Poincare group in the limit of zero acceleration,is proposed.Classical solution of the relativistic length expansion in general accelerated system revisited.

Abstract:
The observational basis of quantum theory in accelerated systems is studied. The extension of Lorentz invariance to accelerated systems via the hypothesis of locality is discussed and the limitations of this hypothesis are pointed out. The nonlocal theory of accelerated observers is briefly described. Moreover, the main observational aspects of Dirac's equation in noninertial frames of reference are presented. The Galilean invariance of nonrelativistic quantum mechanics and the mass superselection rule are examined in the light of the invariance of physical laws under inhomogeneous Lorentz transformations.

Abstract:
Acceleration-induced nonlocality is discussed and a simple field theory of nonlocal electrodynamics is developed. The theory involves a pair of real parameters that are to be determined from observation. The implications of this theory for the phenomenon of helicity-rotation coupling are briefly examined.

Abstract:
We present a new quantum algebraic description of an electron localized in space-time. Positions in space and time, mass and Clifford generators are defined as quantum operators. Commutation relations and relativistic shifts under frame transformations are determined within a unique algebraic framework. Redshifts, i.e. shifts under transformations to uniformly accelerated frames, are evaluated and found to differ from the expressions of classical relativity.

Abstract:
We define quantum observables associated with Einstein localisation in space-time. These observables are built on Poincare' and dilatation generators. Their commutators are given by spin observables defined from the same symmetry generators. Their shifts under transformations to uniformly accelerated frames are evaluated through algebraic computations in conformal algebra. Spin number is found to vary under such transformations with a variation involving further observables introduced as irreducible quadrupole momenta. Quadrupole observables may be dealt with as non commutative polarisations which allow one to define step operators increasing or decreasing the spin number by unity.

Abstract:
A new kind of uniformly accelerated reference frames with a line-element different from the M{\o}ller and Rindler ones is presented, in which every observer at $x, y, z=$consts. has the same constant acceleration. The laws of mechanics are checked in the new kind of frames. Its thermal property is studied. The comparison with the M{\o}ller and Rindler uniform accelerated reference frames is also made.