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The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
On basis of an algebraic analysis of symmetry breaking in general and the Higgs mechanism in the standard model of elementary particles we generalize the concept of symmetry breaking to systems with non-compact groups but not necessarily…
In a previous paper we extended the Lorentz group to include a set of Dirac boosts that give a direct correspondence with a set of generators which for spin 1/2 systems are proportional to the Dirac matrices. The group is particularly…
A new synthesis of the principles of relativity and quantum mechanics is developed by replacing the Poincar\'e group for the de Sitter one. The new relativistic quantum mechanics is an indefinite mass theory which is reduced to the standard…
The infinite group of deformed diffeomorphisms of the spacetime continuum is put into the basis of the gauge theory of gravity. This gives rise to some new ways for unification of gravity with other gauge interactions.
The quark masses evaluated by the Particle Data Group are consistent with terms in a geometric progression of mass values descending from the Planck Mass. The common ratio of the sequence is 2/pi. The quarks occupy the 'principal' levels of…
We construct the action of a relativistic spinning particle from a non-linear realization of a space-time odd vector extension of the Poincar\'e group. For particular values of the parameters appearing in the lagrangian the model has a…
The mathematical foundations of relativistic quantum mechanics is largely based upon the discovery of the Pauli and Dirac matrices. An algebra which lies at an even more fundamental level is the geometric Clifford algebra with metric…
We derive a geometrical approach to produce the mass of particles that could be suitably tested at LHC. Starting from a 5D unification scheme, we show that all the known interactions could be suitably deduced as an induced symmetry breaking…
Symplectic unitary representations for the Poincar\'{e} group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space…
A new concept of geometrization of electromagnetic field is proposed. Instead of the concept of extended field and its point sources, the interacting Maxwellian and Dirac electron--positron fields are considered as a microscopic unified…
Dynamics of the structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The expression…
A toy model for the electroweak interactions(without chirality) is proposed in a six dimensional spacetime with 3 timelike and 3 spacelike coordinates. The spacetime interval $ds^2=dx_\mu dx^\mu$ is left invariant under the symmetry group…
The Dirac equation with chiral symmetry is derived using the irreducible representations of the Poincar\'{e} group, the Lagrangian formalism, and a novel method of projection operators that takes as its starting point the minimal assumption…
There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and…
Observed physical phenomena can be described well by quantum mechanics or general relativity. People may try to find an unified fundamental theory which mainly aims to merge gravity with quantum theory. However, difficulty in merging those…
We investigate the problem of defining group or loop structures on spheres, where by ''sphere'' we mean the level set q(x) = c of a general K-valued quadratic form q, for an invertible scalar c. When K is a field and q non-degenerate, then…
In this paper we present the state of the art about the quarks: group SU(3), Lie algebra, the electric charge and mass. The quarks masses are generated in the same way as the lepton masses. It is constructed a term in the Lagrangian that…
We consider a specific dynamical system of groups formation. It is based simultaneously on a gradient competition between groups and a strong accumulation inside groups. Such a dynamical system demonstrates interesting behavior of densities…
A version of the Dirac equation is derived from first principles using a combination of quaternions and multivariate 4-vectors. The nilpotent form of the operators used allows us to derive explicit expressions for the wavefunctions of free…