Superfield Hamiltonian quantization in terms of quantum antibrackets

We develop a new version of the superfield Hamiltonian quantization. The main new feature is that the BRST-BFV charge and the gauge fixing Fermion are introduced on equal footing within the sigma model approach, which provides for the actual use of the quantum/derived antibrackets. We study in detail the generating equations for the quantum antibrackets and their primed counterparts. We discuss the finite quantum anticanonical transformations generated by the quantum antibracket.

FIRST-CLASS APPROACHES TO MASSIVE 2-FORMS

Massive 2-forms are analyzed from the point of view of the Hamiltonian quantization using the gauge-unfixing approach and respectively the Batalin–Fradkin method. Both methods finally output the manifestly Lorentz covariant path integral for 1- and 2-forms with Stückelberg coupling.

Quantization of an Integrable Minisuperspace Model in Dilaton-Einstein Gravity

We quantize the minisuperspace model of Einstein gravity plus dilaton that describeseither a static spherically symmetric configuration or a Kantowski–Sachs like universe. We develop the canonical formalism and identify canonical quantities that generate rigid symmetries of the Hamiltonian. Quantization is performed both by the Dirac and the reduced methods. Since the system is classically integrable we show that both approaches lead to the same positive definite Hilbert space.