A candidate for a realistic relativistic quantum theory is the hypersurface Bohm-Dirac model. Its formulation uses a foliation of space-time into space-like hypersurfaces. In order to apply the theory and to make contact with the usual quantum formalism, one needs a framework for the description of subsystems. The presence of spin together with the foliation renders the subsystem description mo...

We study quantum field models in indefinite metric. We introduce the modified Wightman axioms of Morchio and Strocchi as a general framework of indefinite metric quantum field theory (QFT) and present concrete interacting relativistic models obtained by analytical continuation from some stochastic processes with Euclidean invariance. As a first step towards scattering theory in indefinite metri...

We analyze the restrictions on distinguishability of quantum states imposed by special relativity. An explicit expression relating the error probability for distinguishing between two orthogonal single-photon states to the time interval T between the beginning of the measurement procedure and the moment when the measurement result is obtained by the observer. Many problems of non-relativistic q...

We comment on the present status, the concepts and their limitations, and the successes and open problems of the various approaches to a relativistic quantum theory of elementary particles, with a hindsight to questions concerning quantum gravity and string theory.

On the basis of the correspondence principle between the relativistic moving medium electrodynamics and relativistic quantum field theory the covari-ant Lagrangian of the electromagnetic field interaction with the polarized spin particles have been obtained. This Lagrangian satisfies the main relativistic quantum field theory requirements and contains four independent covariant spin structures,...

We shall outline two ways of introducing the modification of Einstein’s relativistic symmetries of special relativity theory the Poincaré symmetries. The most complete way of introducing the modifications is via the noncocommutative Hopfalgebraic structure describing quantum symmetries. Two types of quantum relativistic symmetries are described, one with constant commutator of quantum Minkowski...

We analyze the restrictions on distinguishability of quantum states imposed by special relativity. An explicit expression relating the error probability for distinguishing between two orthogonal single-photon states to the time interval T between the beginning of the measurement procedure and the moment when the measurement result is obtained by the observer. Many problems of non-relativistic q...

Two different strategies of the relativistic quantum theory construction are considered and evaluated. The first strategy is the conventional strategy, based on application of the quantum mechanics technique to relativistic systems. This approach cannot solve the problem of pair production. The apparent success of QFT at solution of this problem is conditioned by the inconsistency of QFT, when ...

From the “vibrating string” and “Kepler’s equation” theories to relativistic quantum fields, (divergent) series resummations, perturbation theory, KAM theory.