Superfield Quantization Method . III . Construction of Quantization Scheme

Quantization procedure in the framework of general superfield quantization method (GSQM), based on the Lagrangian [1] and Hamiltonian [2] formulations for general super-field theory of fields, for irreducible gauge theories in Lagrangian formalism is proposed. Extension procedure for supermanifold M cl of superfields A ı (θ), ghost number construction are considered. Classical and ¯ h-deformed generating (master) equations, existence theorems for their solutions are formulated in T * odd M min , T * odd M ext. Analogous scheme is realized for BV similar generating equations. Master equations versions for GSQM and BV similar scheme are deformed in powers of superfields • Γ p (θ) = (• Φ B (θ), • Φ * B (θ)) into supermanifold T odd (T * odd M ext). Arbitrariness in a choice of solutions for these equations is described. Investigation of formal Hamiltonian systems for II class theories [2] defined via corresponding master equations solutions is conducted. Gauge fixing for those theories is described by two ways. Functional integral of superfunctions on T odd (T * odd M ext) is defined. Properties for generating functionals of Green's superfunctions are studied. θ-component quantization formulation, connection with BV method and superfield quantization [3] are established. Quantization scheme realization is demonstrated on 6 models. Lagrangian and Hamiltonian formulations for general superfield theory of fields (GSTF) formulated in papers [1,2] directly appear by the basis for creation of GSQM rules for gauge theories in Lagrangian (in the usual sense) formalism generalizing in a natural way the rules for BV quantization method [4] in the superfield form. In this case a procedure for GSQM is realized for irreducible superfield (on θ) gauge model in the Hamiltonian (or not always equivalently in Lagrangian) formulation for GSTF. The last as it had been noticed in [2] contains the all information, among them, on an usual (relativistic) field theory model. Not repeating the * motivations for creation of GSTF and GSQM stated in detail in [1] let us point out that by the paper's aim is the construction of complete and noncontradictory rules for GSQM in the Lagrangian formalism in the framework of GSTF. In Sec.II having partially preparatory nature it is considered an algorithm, connected with gauge invariance, of extension of the supermanifold M cl and superalgebras defined on M cl including operatorial ones. Group-theoretic construction of the ghost number concept is realized in Sec.III. Sec.IV is devoted to formulation of …