New methods in the theory of gauge fields

TL;DR

This paper proposes a new approach to gauge field theory by reversing the traditional construction process, emphasizing the derivation of total Lagrangians from fundamental principles rather than starting from free fields.

Contribution

It introduces a method to construct total Lagrangians based on the minimization of variance of theoretical fields, contrasting with the conventional gauge formalism.

Findings

Differentiates between 'theoretical' and 'empiric' wave-functions.

Suggests minimizing the variance of differential operators on fields.

Proposes a reverse construction principle for gauge theories.

Abstract

One of the fundamental problems of the theoretical physics is the search of the axioms, which ought to be the basis for the one-valued construction of Lagrangians of the relativistic fields. The creation of the gauge fields theory was the great success in the solution of this problem. The gauge formalism allowed to derive the total Lagrangians of the interacting fields from the postulated Lagrangians of the noninteracting (free) fields. We offer to do quite the reverse in consequence of what it is necessary to seek from the out set the construction principles of the total Lagrangians. By the theory construction we shall differ the wave-functions being the solutions of the differential equations (``theoretical'' functions) from the wave-functions which is constructed on the base of the experimental data possibly received by a scattering of particles (``empiric'' functions). The ``empiric'' functions are necessary only for the definition (it is possibly only approximately) of the transition operators which will affect at the ``theoretical'' functions. This operators will be approximated the differential operators so, that the generalized variance of the differentiable ``theoretical'' fields will be the minimal one.