相关论文: An Octonionic Gauge Theory

A geometric model for nonholonomic Lagrangian field theory is studied. The multisymplectic approach to such a theory as well as the corresponding Cauchy formalism are discussed. It is shown that in both formulations, the relevant equations…

The algebra of octonions is non-associative (as well as non-commutative). This makes it very difficult to derive algebraic results, and to perform computation with octonions. Given a product of more than two octonions, in general, the order…

Language theory, symbolic dynamics, modelisation of viral insertion into the genetic code of a host cell motivate the introduction of new types of bialgebras whose coalgebra parts are not necessarily coassociative. One of the aim of this…

As is well-known, the real quaternion division algebra $ {\cal H}$ is algebraically isomorphic to a 4-by-4 real matrix algebra. But the real division octonion algebra ${\cal O}$ can not be algebraically isomorphic to any matrix algebras…

We consider a generalization of nonrelativistic Schr\"odinger-Higgs Lagrangian by introducing a nonstandard kinetic term. We show that this model is Galilean invariant, we construct the conserved charges associated to the symmetries and…

We consider the conformal gauging of non-abelian groups. In such cases there are inequivalent ways of gauging (generalizing the axial and vector cases for abelian groups) corresponding to external automorphisms of the group. Different…

Abelian Gauge Theories are quantized in a geometric representation that generalizes the Loop Representation and treates electric and magnetic operators on the same footing. The usual canonical algebra is turned into a topological algebra of…

We investigate a non-trivial extension of the $D-$dimensional Poincar\'e algebra. Matrix representations are obtained. The bosonic multiplets contain antisymmetric tensor fields. It turns out that this symmetry acts in a natural geometric…

A non-Abelian gauge field framework is proposed using the hypercomplex ring formalism. This extension generates non-compact hyperbolic symmetries, which, alongside the compact gauge symmetries, double the internal degrees of freedom. This…

A new representation of Lagrangians of 4D nonlinear electrodynamics is considered. In this new formulation, in parallel with the standard Maxwell field strength F, an auxiliary bispinor (tensor) field V is introduced. The gauge field…

In the two papers of this series, we initiate the development of a new approach to implementing the concept of symmetry in classical field theory, based on replacing Lie groups/algebras by Lie groupoids/algebroids, which are the appropriate…

Using octonions, more specifically, using a 4 x 4 matrix representation of octonions obtained with the help of algebraic properties of quaternions, we obtain the fully symmetric Maxwell's equations (Maxwell's equations with electric and…

A presentation by generators and relations of the $n$th symmetric power $B$ of a commutative algebra $A$ over a field of characteristic zero or greater than $n$ is given. This is applied to get information on a minimal homogeneous…

We study the representation theory of finite-dimensional $\omega$-Lie algebras over the complex field. We derive an $\omega$-Lie version of the classical Lie's theorem, i.e., any finite-dimensional irreducible module of a soluble…

A new Lagrangian realizing the symmetry of the M Algebra in eleven-dimensional space-time is presented. By means of the novel technique of Abelian Semigroup Expansion, a link between the M Algebra and the orthosymplectic algebra osp(32|1)…

Endomorphisms algebras can replace the concept of principal fiber bundle. Gauge theories are reformulated within this algebraic framework and further generalized to unify ordinary connections and Higgs fields. A 'noncommutative Maxwell'…

We suggest an extension of the gauge principle which includes tensor gauge fields. The extended non-Abelian gauge transformations of the tensor gauge fields form a new large group. On this group one can define field strength tensors, which…

We announce a new approach to the octonions as quasiassociative algebras. We strip out the categorical and quasi-quantum group considerations of our longer paper and present here (without proof) some of the more algebraic conclusions

Motivated by a recent progress in studying the duality-symmetric models of nonlinear electrodynamics, we revert to the auxiliary tensorial (bispinor) field formulation of the O(2) duality proposed by us in arXiv:hep-th/0110074,…

Starting with the generalized field equation of dyons and gravito-dyons, we study the theory of octonion variables to the SU (2) non-Abelian gauge formalism. We demonstrate the resemblance of octonion covariant derivative with the gauge…