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An introduction to the minimal supersymmetric Standard Model (MSSM) is given. The motivation for “low-energy” supersymmetry is reviewed, and the structure of the MSSM is outlined. In its most general form, the MSSM can be viewed as a low-energy effective theory parametrized by a set of arbitrary soft-supersymmetry-breaking parameters. A variety of techniques for reducing the parameter freedom o...

Dirac’s theory is not the unique consistent with physical principles specific of a free spin-one-half particle. In fact, we derive classes theories an elementary particle from principle Poincaré’s invariance and covariance position. The Dirac just one these theories, characterized by singular predictions, namely, zitterbewegung. Yet, class here derived contains families without predictions. For...

T he standard model of particle physics describes all the known elementary particles, like electrons and quarks. Many of these particles have analogs in condensed matter, where they arise as collective states, or quasiparticles. One example is an electronic state in graphene that behaves like a massless Dirac fermion—a spin-1/2 particle that is not its own antiparticle. But condensed-matter phy...

It is shown, that our contemporary knowledge of geometry is insufficient, because we know only axiomatizable geometries. With such a knowledge of geometry one cannot investigate properly physics of microcosm and structure of elementary particles. One can obtain only a phenomenological systematics of elementary particles, whose construction does not need a discrimination mechanism. The discrimin...

The Standard Model of the theory of elementary particles is based on the U(1) × SU(2) × SU(3) symmetry. In the presence of a gravitation field, i. e. in a non-flat space-time manifold, this symmetry is implemented through three special vector bundles. Connections associated with these vector bundles are studied in this paper. In the Standard Model they are interpreted as gauge fields. 1. The U ...

In these lectures I give a short review of the main theoretical ideas underlying the extensions of the Standard Model of elementary particle interactions.

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 caused by a potential. Thereto we give some simple, but unfamiliar examples of symmetry breaking with and without potentials. The analysis of the concept of ma...

In this chapter a double tensor index k implies summation from 1 to 4. There is no classical way to treat the spin and charge variables of elementary particles. ' Therefore we represent matter by a set of complex wave fields p„. The quantities J, and S„& occurring in (1.1) are formed from matrices j„and s„A, . if I =0. Eq. (1.3) takes the form of Dirac's equation for a particle with inherent ma...