Modification of the Scalar QED Lagrangian over Doublets in a Space of Variable Dimension and Its Connection with the Higgs Lagrangian

In [1-6] the construction of an algebraic framework is presented that allows one to take into account the possibility of a change in the dimension of the configuration space, and a modification of some equations of mathematical physics is carried out. The modification of some equations (for example, the Dirac equation [4]) is due to a correction of the form of the covariant derivative, which, owing to the indicated possibility of a change of the dimension of the space on which it is defined, acquires an additional term containing information about the dimension jump. Here the constructed space of variable dimension itself is non-Riemannian, while its factor subspace constructed for a fixed value of the dimension possesses the Riemannian property. This construction leads to initially unexpected effects. Of particular interest is the confirmation of the physicality of such a configuration space, obtained in the course of preliminary experiments. In the present work a modification of the scalar QED Lagrangian constructed over a field of doublets is considered, and a comparison of the obtained result with the Higgs Lagrangian is carried out. It is shown that formally taking into account the possibility of a change of the dimension of the configuration space in accordance with the algebraic construction [1-4] in the case of a scalar QED field leads to the Higgs Lagrangian under the assumption of the existence of constant periodic and anharmonic oscillations of the dimension of the configuration space associated with the problem.