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Binary symmetry constraints of the N-wave interaction equations in 1+1 and 2+1 dimensions are proposed to reduce the N-wave interaction equations into finite-dimensional Liouville integrable systems. A new involutive and functionally…
A modified version of the bilocal particle is presented in terms of complex space time. Unusual constraint structure of the model is studied, and a new concept of the physical equivalence is proposed in accordance with Dirac's conjecture.…
It is commonly accepted that in hadronic or nuclear collisions at extremely high energies the shortest scales are explored. At the classical level, this property of the interaction is closely related to the Lorentz contraction of the fields…
We introduce a new term into the Dirac equation based on the Lorentz symmetry violation background in order to make a theoretical description of the relativistic quantum dynamics of a spin-half neutral particle, where the wave function of…
We investigate wavepacket dynamics across supercritical barriers for the Klein-Gordon and Dirac equations. Our treatment is based on a multiple scattering expansion (MSE). For spin-0 particles, the MSE diverges, rendering invalid the use of…
The Standard Model of particle physics was established based on the equivalence principle and gauge invariance. The Lagrangians were built upon experimental data demonstrating the violation of discrete symmetries together with ideas of…
We introduce and analyze a system of relativistic fermions in a space-time continuum, which interact via an action principle as previously considered in a discrete space-time. The model is defined by specifying the vacuum as a sum of Dirac…
It is shown that the phenomenon of irreversibility in many-body and few-body systems can be explained and described within the framework of the concept of direct (not instantaneous) interaction of particles without using probabilistic…
In recent years, an extensive survey on various wave equations of relativistic quantum mechanics with different types of potential interactions has been a line of great interest. In this regime, special attention has been given to the Dirac…
We review the main concepts of the recently introduced principle of relative locality and investigate some aspects of classical interactions between point particles from this new perspective. We start with a physical motivation and basic…
It is well known that nonrelativistic quantum mechanics presents a clear asymmetry between space and time. Much of this asymmetry is attributed to the lack of Lorentz invariance of the theory. Nonetheless, a recent work [Phys. Rev. A…
General solutions of relativistic wave equations are studied in terms of the functions on the Lorentz group. A close relationship between hyperspherical functions and matrix elements of irreducible representations of the Lorentz group is…
Interest on 2 + 1 dimensional electron systems has increased considerably after the realization of novel properties of graphene sheets, in which the behaviour of electrons is effectively described by relativistic equations. Having this fact…
Powerful general arguments allow only a few families of long-range interactions, exemplified by gauge field theories of electromagnetism and gravity. However, all of these arguments presuppose that massless fields have zero spin scale…
An approximate quantum-mechanical two-body equation for spinless particles incorporating relativistic kinematics is derived. The derivation is based on the relativistic energy-momentum relation $mc^{2}+\epsilon =…
An approach to special relativistic dynamics using the language of spinors and twistors is presented. Exploiting the natural conformally invariant symplectic structure of the twistor space, a model is constructed which describes a…
In this article we considered models of particles living in a three-dimensional space-time with a nonstandard noncommutativity induced by shifting canonical coordinates and momenta with generators of a unitary irreducible representation of…
We show in this paper that the dynamics of a non-relativistic particle with spin, coupled to an external electromagnetic field and to a background that breaks Lorentz symmetry, is naturally endowed with an N=1-supersymmetry. This result is…
Massive and massless Dirac equations with Lorentz-covariant cubic nonlinearities are considered in spatial dimension $d=2,3$. Global well-posedness of the Cauchy problem for small initial data in scale-invariant Sobolev spaces and…
After a review of the problems induced by the Lorentz signature of Minkowski space-time, like the need of a clock synchronization convention for the definition of 3-space and the complexity of the notion of relativistic center of mass,…