Basic Theorem, Gauge Algebra, $\theta$-superfield QED in the Lagrangian Formulation of General Superfield Theory of Fields

TL;DR

This paper proves a fundamental theorem in superfield theory, explores gauge transformations and algebra, and constructs a superfield model generalizing QED within the Lagrangian framework.

Contribution

It establishes the basic theorem of superfield Lagrangian formulation, analyzes gauge algebra structures, and develops a generalized superfield model extending QED.

Findings

Proved the basic theorem of superfield Lagrangian formulation.

Analyzed gauge transformations and their algebra in superfield theories.

Constructed a superfield model generalizing QED with Abelian gauge algebra.

Abstract

The basic theorem of the Lagrangian formulation for general superfield theory of fields (GSTF) is proved. The gauge transformations of general type (GTGT) and gauge algebra of generators of GTGT (GGTGT) as the consequences of the above theorem are studied. It is established the gauge algebra of GGTGT contains the one of generators of gauge transformations of special type (GGTST) as one's subalgebra. In the framework of Lagrangian formulation for GSTF the nontrivial superfield model generalizing the model of Quantum Electrodynamics and belonging to the class of gauge theory of general type (GThGT) with Abelian gauge algebra of GGTGT is constructed.