Gauge theory of second class constraints without extra variables

We show that any theory with second class constraints may be cast into a gauge theory if one makes use of solutions of the constraints expressed in terms of the coordinates of the original phase space. We perform a Lagrangian path integral quantization of the resulting gauge theory and show that the natural measure follows from a superfield formulation.Comment: 12 pages, Latexfil

Path Integral Formulation with Deformed Antibracket

We propose how to incorporate the Leites-Shchepochkina-Konstein-Tyutin deformed antibracket into the quantum field-antifield formalism.Comment: 13 pages, LaTeX. v2: Added references. To appear in Phys. Lett.

Reparametrization-Invariant Effective Action in Field-Antifield Formalism

We introduce classical and quantum antifields in the reparametrization-invariant effective action, and derive a deformed classical master equation.Comment: 14 pages, LaTeX. v2: Further observations, Added one appendix. v3: Version submitted to IJMPA. v4: Version published in IJMP

Odd Scalar Curvature in Field-Antifield Formalism

We consider the possibility of adding a Grassmann-odd function \nu to the odd Laplacian. Requiring the total \Delta operator to be nilpotent leads to a differential condition for \nu, which is integrable. It turns out that the odd function \nu is not an independent geometric object, but is instead completely specified by the antisymplectic structure E and the density \rho. The main impact of introducing the \nu term is that it makes compatibility relations between E and \rho obsolete. We give a geometric interpretation of \nu as (minus 1/8 times) the odd scalar curvature of an arbitrary antisymplectic, torsion-free and \rho-compatible connection. We show that the total \Delta operator is a \rho-dressed version of Khudaverdian's \Delta_E operator, which takes semidensities to semidensities. We also show that the construction generalizes to the situation where \rho is replaced by a non-flat line bundle connection F. This generalization is implemented by breaking the nilpotency of \Delta with an arbitrary Grassmann-even second-order operator source.Comment: 23 pages, LaTeX. v2: More material added. v3: Reference added. v4: Grant number added. v5: Minor changes. v6: Stylistic change

Projection operator approach to general constrained systems

We propose a new BRST-like quantization procedure which is applicable to dynamical systems containing both first and second class constraints. It requires no explicit separation into first and second class constraints and therefore no conversion of second class constraints is needed. The basic ingredient is instead an invariant projection operator which projects out the maximal subset of constraints in involution. The hope is that the method will enable a covariant quantization of models for which there is no covariant separation into first and second class constraints. An example of this type is given.Comment: 12 pages, Latexfile,minor misprints correcte

Closed description of arbitrariness in resolving quantum master equation

In the most general case of the Delta exact operator valued generators constructed of an arbitrary Fermion operator, we present a closed solution for the transformed master action in terms of the original master action in the closed form of the corresponding path integral. We show in detail how that path integral reduces to the known result in the case of being the Delta exact generators constructed of an arbitrary Fermion function.Comment: 13 pages, v2: Section 2 extended, misprint corrected, references added, formula on page 7 corrected, new formula (4.30) and a phrase on it inserted, v3: misprints in formulas (2.12), (4.23), (4.36)-(4.39) corrected, v4: formulae (A.8), (A.11), (A.12) added, v5:published versio