Lagrangian Formalism of θ-Superfield Theory of Fields

The rules for constructing Lagrangian formulation for θ-superfield theory of fields (θSTF) are introduced and considered on the whole in the framework of proposed here new general superfield quantization method for general gauge theories. Algebraic, group-theoretic and analytic description aspects for supervariables over (Grassmann) algebras containing anticommuting generating element θ and interpreted further in particular as an ”odd” time are examined. Superfunction SL(θ) ≡ SL ( A(θ), dA(θ) dθ , θ ) and its global symmetries are defined on the extended space (supermanifold) ToddMcl×{θ} parameterized by local coordinates: superfields Aı(θ), dA (θ) dθ , θ. Extremality properties of the superfunctional Z[A] = ∫ dθSL(θ) are analyzed together with properties of corresponding Euler-Lagrange equations. System of definitions for Lagrangian formulation of θ-STF including extension of gauge invariance concept is suggested. The direct and inverse problems of zero locus reduction for extended (anti)symplectic manifolds over Mmin = {(A ı(θ), Cα(θ))}, with (odd) even brackets, corresponding to initial (special) general type θ-superfield models are employed to construct iteratively the new interconnected models both embedded into manifolds above with reduced brackets and enlarging them with continued ones. Component (on θ) formulation for θ-STF variables and operations is produced providing the connection with standard gauge field theory. Realization of θ-STF constructions is demonstrated on models of scalar, spinor, vector superfields which are used to formulate the θ-superfield model with abelian two-parametric gauge supergroup generalizing the θ-superfield quantum electrodynamics. PACS codes: 03.50.-z, 11.10.Ef, 11.15.-q, 12.20.-m