Generalization of Lagrangian of electro-weak interaction to the octonionic algebra

In the article it is considered the extension of Weinberg-Salam theory from SU(2) group to the octonionic algebra. The extended octonionic algebra is used as particle wave function instead of spinors on su(2). It is shown, that leads to appearance of a new neutral massive vector C and E-bosons (peculiar property of the E-boson is that it does not interact with matter), and two charged massive vector D and D∗ bosons. Introduction The progress in extending physical theory to octonionic algebra is related with developing of works [1] and [2], where useful matrix representation of nonassociative algebra was suggested. The tax for using matrix view was an unusual multiplication law. Therefore, according to Feinmann interpretation of quantum particle motion in extern field, although there is no charge, during the particle movement its condition alternates and the alternation is caused by non-associative interaction nature. Perhaps, the first time octonionic algebra was applied to the question in work [3], where octonionic the science of quantum mechanics was introduced. Some scientists connect extended algebra with extended space-time interpretation [4]. Also, a range of scientists regard the extension as deriving new properties in the network of electromagnetic theory (e.g. in [6]). The interpretation of this new type of interaction, in terms of fields, could be found in [7]. Meanwhile, the research over the relation of the new types of interaction with the conventional ones, as far as the author is concerned, has not ever taken place. Dep. of Math., SPb SUEF, Sadovaya 21, 191023, St.Petersburg, Russia, E-mail: [email protected]