Harmonic BRST quantization of systems with irreducible holomorphic bosonic and fermionic constraints.

Abstract

We consider systems with second-class constraints or, equivalently, first-class holomorphic constraints. We show that the harmonic Becchi-Rouet-Stora-Tyutin method of quantizing systems with bosonic holomorphic constraints extends to systems having both bosonic and fermionic holomorphic constraints. The ghosts for bosonic holomorphic constraints in the harmonic BRST method have a Poisson brackets structure different from that of the ghosts in the usual BRST method, which applies to systems with real first-class constraints. Apart from this exotic ghost structure for bosonic constraints, the new feature of the harmonic BRST method is the introduction of two new holomorphic BRST charges \ensuremath{\bigominus} and $\overline{\ensuremath{\bigominus}}$ and the addition of an extra term $\ensuremath{-}\ensuremath{\beta}{\ensuremath{\bigominus}, \overline{\ensuremath{\bigominus}}}$ to the BRST-invariant Hamiltonian. We apply the Fradkin-Vilkovisky theorem to general systems with mixed bosonic and fermionic holomorphic constraints and show that, taking an appropriate limit, the extra term in the harmonic BRST-modified path integral reproduces the correct Senjanovic measure.