相关论文: The Dirac algebra and grand unification

A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…

Algebraic scheme for constructing deformations of structure constants for associative algebras generated by a deformation driving algebras (DDAs) is discussed. An ideal of left divisors of zero plays a central role in this construction.…

The most general 2+1 dimensional spinning particle model is considered. The action functional may involve all the possible first order Poincare invariants of world lines, and the particular class of actions is specified thus the…

In the report submitted here, an elementary formula is presented that allows calculation of the fine structure constant, derived on the basis of the unified theory of the electromagnetic and gravitational field elaborated by the author.…

The unification of gauge couplings suggests that there is an underlying (supersymmetric) unification of the strong, electromagnetic and weak interactions. The prediction of the unification scale may be the first quantitative indication that…

This is an introduction to linear algebra and group theory. We first review the linear algebra basics, namely the determinant, the diagonalization procedure and more, and with the determinant being constructed as it should, as a signed…

After a revision of the main features of the structure of the Dirac electron a plausible definition of elementary particle is stated. It is shown that this definition leads in the classical case to a picture which produces a very clear…

We introduce linear Dirac and generalized complex structures on Cartan geometries and give criteria for Dirac subalgebras of $\frkg\ltimes\frkg^*$ representing Dirac structures on a Cartan geometry. We prove that there is a bijection…

A simple translation between a standard representation of $\mathfrak{sl}_2\mathbb{C}$ and the complex-quaternions ($\mathbb{H}\otimes_\mathbb{R}\mathbb{C}$) is established and exploited to construct a novel hyper-complex description of the…

In this paper, we review the construction of the Dirac operator for graded affine Hecke algebras and calculate the Dirac cohomology of irreducible unitary modules for the graded Hecke algebra of gl(n).

Symmetry, in particular gauge symmetry, is a fundamental principle in theoretical physics. It is intimately connected to the geometry of fibre bundles. A refinement to the gauge principle, known as ``spontaneous symmetry breaking'', leads…

Dirac's equation of the electron will be discussed by using quaternions as the basis of a new formalism which seems to be very well adapted to the problem. The transformation properties of the equations as well as the invariant and…

We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…

The concept of a Dirac algebroid, which is a linear almost Dirac structure on a vector bundle, was designed to generate phase equations for mechanical systems with linear nonholonomic constraints. We apply it to systems with magnetic-like…

We rewrite the 1+1 Dirac equation in light cone coordinates in two significant forms, and solve them exactly using the classical calculus of finite differences. The complex form yields ``Feynman's Checkerboard''---a weighted sum over…

Charge symmetry breaking in the strong interaction occurs because of the difference between the masses of the up and down quarks. At present the Standard Model can't explain the observed mass pattern (M(n), M(p), m(u), m(d) etc.) and their…

In this article we analyze the structure of the semigroup of inner perturbations in noncommutative geometry. This perturbation semigroup is associated to a unital associative *-algebra and extends the group of unitary elements of this…

A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta…

We are interested in four-dimensional Dirac-Klein-Gordon equations, a fundamental model in particle physics. The main goal of this paper is to establish global existence of solutions to the coupled system and to explore their long-time…

Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…