I.A. Batalin

Operational quantization of dynamical systems subject to second class constraints

Abstract An operational version is proposed for the generalized canonical quantization method of dynamical systems subject to second class constraints. New generating equations are formulated for the generalized algebra of constraints and for the unitarizing hamiltonian.

Closure of the gauge algebra, generalized lie equations and Feynman rules

Abstract A method is given by which an open gauge algebra can always be closed and even made abelian. As a preliminary the generalized Lie equations for the open group are obtained. The Feynman rules for gauge theories with open algebras are derived by reducing the gauge theory to a non-gauge one.

Another version for operatorial quantization of dynamical systems with irreducible constraints

Abstract An alternative version is proposed for operational canonical quantization of dynamical systems subject to irreducible first- and second-class constraints, and which exploits a modified way of defining the extra degrees of freedom needed for conversion of the original second-class constraints to (effective) first-class constraints. The alternative version considered is shown to be canonically equivalent to the previously suggested formulation. It is also shown that both formulations belong to an infinite class of canonically-equivalent solutions of the basic generating equations which correspond to the most general effective constraints.

Generalized Canonical Quantization of Dynamical Systems With Constraints and Curved Phase Space

Abstract The operator version of generalized canonical quantization is formulated for dynamical systems with irreducible constraints and curved phase space.

Quantum geometry of symbols and operators

Abstract A coordinate-invariant scheme of geometrical quantization in the nondegenerate case and in the presence of constraints is proposed. No additional variables are introduced. In both cases, the explicit formula of associative ∗-multiplication of symbols is found. The operators are assigned to symbols and vice versa. A geometrically adequate version of canonical commutation relations in the nondegenerate case and their Dirac analogue in the presence of constraints are found.

An infinite algebra of quantum Dirac brackets

Abstract A new algebraic approach to the theory with second-class constraints is proposed. The operator equations that generate automatically the infinite algebra of quantum Dirac brackets are formulated. First-class constraints are naturally involved into the new algebraic scheme.

Operator quantization of dynamical systems with curved phase space

Abstract The operator quantization method is extended to dynamical systems with curved phase space by treating them effectively as those with a flat phase space of the double dimension and effective second-class constraints.

Quantization of gauge theories with open algebra in the representation with the third ghost

We suggest a modified representation of the general BRS construction [1], which gives in a closed form the quantization of gauge theories with open algebra. Instead of gauging the Lagrange multiplier in this representation, we have the third ghost πα which appears in the quantization procedure on equal footing with the Faddeev-Popov ghosts Cα, Cα. This new representation is especially convenient in the non-singular gauges of the form 12γαβXβXα, where both Xα and γαβ may arbitrarily depend on quantum fields. In the closed algebra case, we recover the result of Nielsen [2], whereas for the theories with open algebra we find new ghost couplings of the form CnCnπm, n = 1,…; m = 0, 1,…,n.

External source in gauge theory

Abstract The correct formulation of Yang-Mills theory is obtained on the basis of the naive Feynman integral into which the external source is introduced in a gauge-invariant way.

A compensating functional method in the massive Yang-Mills theory

In the massive and massless Yang-Mills theories the generating functional (the S-matrix) independence of the gauge parameter is provided on the mass shell without introducing an extra degree of freedom (gauge group integration).