Notes on the Quantization of the Complex Linear Superfield

The quantization of the complex linear superfield requires an infinite tower of ghosts. Using the Batalin-Vilkovisky technique, Grisaru, Van Proeyen, and Zanon have been able to define a correct procedure to construct a gauge-fixed action. We generalize their technique by introducing the Lagrange multipliers into the non-minimal sector and we study the characteristic BRST cohomology. We show how the physical subspace is singled out. Finally, we quantize the model in the presence of a background and of a quantum gauge superfield.