In this paper finite-dimensional Lorentz covariant bifurcation equations are constructed and their properties, solutions, and gradient structures are examined. The possible applications of these ideas and techniques to elementary particle physics are considered.

Several modification of Einstein’s general relativity have been proposed and extensively studied so far by many cosmologists to unify gravitation and many other effects in the universe. Barber 1 has produced two continuous self-creation theories by modifying the Brans-Dicke theory and general relativity. The modified theories create the universe out of self-contained gravitational and matter fi...

In these lectures I present a basic introduction to supersymmetry, especially to N = 1 supersymmetric gauge theories and their renormalization, in the Wess-Zumino gauge. I also discuss the various ways supersymmetry may be broken in order to account for the lack of exact supersymmetry in the actual world of elementary particles. On leave of absence from: Département de Physique Théorique – Univ...

We consider the possibility of using measurements of anomalous magnetic moments of elementary particles as a possible test of the Einstein Equivalence Principle (EEP). For the class non-metric theories of gravity described by the T Hǫµ formalism we find several novel mechanisms for breaking the EEP, and discuss the possibilities of setting new empirical constraints on such effects.

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.

We study the interplay of supersymmetry and certain non-compact invariance groups in extended supergravity theories (ESGTs). We use the N = 4 ESGT . to demonstrate that these symmetries do not commute and exhibit the infinite dimensional superinvariance algebra generated by them in the rigid limit. Using this result, we look for unitary representations of the full algebra. We discuss the implic...

Using concepts of physics of elementary particles concerning the breaking of symmetry and grannd unified theory we propose to study with the algebraic approximation the degeneracy finded in the genetic code with the incorporation of a horizontal symmetry used in gauge theories to fit the contents of the multiplets of the genetic code. It is used the algebraic approch of Hornos et. al. [1, 2, 3,...

Extensions of the Standard Model of elementary particle physics to noncommutative geometries have been proposed as a low energy limit of string models. Independent of this motivation, one may consider such a model as an effective field theory with higher-dimensional operators containing an antisymmetric rank-two background field. We study the signals of such a Noncommutative Standard Model (NCS...

The recent apparent observation [1, 2] of the Higgs boson [3, 4, 5, 6] has led to much interest in the popular claim that the Higgs boson (or better, the Higgs field) “gives mass” to those elementary particles that have it. Discuss how the de Broglie relations [7] for “matter waves” lead to a wave equation with a term that depends on mass, and that interpretation of this term as due to the inte...

One of the major goals of the Large Hadron Collider is to probe the electroweak symmetry breaking mechanism and the generation of the masses of the elementary particles. We review the physics of the Higgs sector in the Standard Model and some of its extensions such as supersymmetric theories and models of extra dimensions. The prospects for discovering the Higgs particles at the LHC and the stu...