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We present a Master equation for description of fermions and bosons for special relativities with two invariant scales, SR2, (c and lambda_P). We introduce canonically-conjugate variables (chi^0, chi) to (epsilon, pi) of Judes-Visser.…
We show that the special relativistic dynamics when combined with quantum mechanics and the concept of superstatistics can be interpreted as arising from two interlocked non-relativistic stochastic processes that operate at different energy…
We investigate some interesting solutions in the DSR theories. These solutions have important features in optics and mechanics. We use these similarities for a better understanding of these theories. We know that, the vacuum in the DSR has…
In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between Loop Quantum Gravity, Causal Dynamical Triangulations,…
There is a one-to-one correspondence between Snyder's model in de Sitter space of momenta and the \dS-invariant special relativity. This indicates that physics at the Planck length $\ell_P$ and the scale $R=3/\Lambda$ should be dual to each…
An outline is presented of the Extended Scale Relativity (ESR) in C-spaces (Clifford manifolds), where the speed of light and the minimum Planck scale are the two universal invariants. This represents in a sense an extension of the theory…
We investigate how deformations of special relativity in momentum space can be extended to position space in a consistent way, such that the dimensionless contraction between wave-vector and coordinate-vector remains invariant. By using a…
This paper presents an approach to the creation of a variant of Extended Special Relativity that takes into consideration the existence of limiting relativistically invariant quantities (Planck parameters). It shows the possibility of…
We study the three-dimensional Dirac and Klein-Gordon equations with scalar and vector potentials of equal magnitudes as an attempt to give a proper physical interpretation of this class of problems which has recently been accumulating…
We propose new noncommutative models of quantum phase spaces, containing a pair of $\kappa$-deformed Poincar\'e algebras, with two independent double ($\kappa,\tilde{\kappa}$)-deformations in space-time and four-momenta sectors. The first…
In this paper -- Part 2 of our series on discrete spacetime -- we first provide a review of the previously published Part 1 that included the first important steps in the development of a new model of discrete spacetime (DST): the Isotropic…
This paper shows the need of the emergence of a universal minimum speed in the space-time by means of a more thorough investigation of Dirac's large number hypothesis (LNH). We will realize that there should be a minimum speed $V$ with the…
In the framework of the most-studied doubly special relativity models the use of the naive formula $v=dE/dp$ has been argued to lead to inconsistencies connected to different rules of transformation, under boosts, of particles with the same…
Deformed Special Relativity is usually presented as a deformation of Special Relativity accommodating a new universal constant, the Planck mass, while respecting the relativity principle. In order to avoid some fundamental problems (e.g.…
Research during the last decade demonstrates that effects originating on the Planck scale are currently being tested in multiple observational contexts. In this review we discuss quantum gravity phenomenological models and their possible…
Assuming the validity of the relativity principle, we discuss the implications on relativistic kinematics of a deformation of the Poincar\'e invariance that preserves the Poincar\'e algebra, and only modifies its action on phase space in a…
An unsolved problem of particle physics is a discrepancy between the measured value of the muon anomalous magnetic moment and the theoretical prediction based on standard quantum electrodynamics. In this paper we show that if spacetime…
Relativistic symmetries of the Dirac Hamiltonian with a mixture of spherically symmetric Lorentz scalar and vector potentials, are examined from the point of view of supersymmetric quantum mechanics. The cases considered include the…
The mathematical treatment and graphical representation of Special Relativity (SR) are well established, yet carry deep implications that remain hard to visualize. This paper presents a new graphical interpretation of the geometry of SR…
General N=(1,1) dilaton supergravity in two dimensions allows a background independent exact quantization of the geometric part, if these theories are formulated as specific graded Poisson-sigma models. The strategy developed for the…