2002/10/22 by A. A. Reshetnyak, Reshetnyak, A. A.
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0210207
50 pages, LaTeX, no figures, title changed, introduction updated, section with zero-locus reduction problems and methods of new superfield models construction added, section with differential equations study with odd operator transferred into appendix, new superfield gauge model, 8 references added, typos corrected
The rules to construct Lagrangian formulation for θ-superfield theory of fields (θ-STF) are introduced and considered on the whole in the framework of new 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), its global symmetries are defined on the extended space Todd\cal Mcl × \θ\ parameterized by superfields \cal A\imath(θ), \fracd\cal A\imath(θ)dθ\phantomxxx, θ. Extremality properties of superfunctional Z[\cal A]=∫ dθSL(θ) and ones of corresponding Euler-Lagrange equations are analyzed. The direct and inverse problems of zero locus reduction for extended (anti)symplectic manifolds over \cal Mmin = \(\cal A\imath(θ), Cα(θ))\, with (odd) even brackets, corresponding to initial 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.