Parent field theory and unfolding in BRST first-quantized terms

For free field theories associated with BRST first-quantized gauge systems, we identify auxiliary fields and pure gauge variables already on the first-quantized level as the fields associated with algebraically contractible pairs for the BRST operator. Locality of the field theory is taken into account by separating the space–time degrees of freedom from the internal ones. A standard extension of the first-quantized system developed to study quantization on curved manifolds is used here for the construction of a first-order parent field theory that can be reduced both to the field theory of the starting point system and to the unfolded formulation used in the context of higher-spin gauge theories. As an illustration, we construct the unfolded form of the Klein-Gordon equation. ∗ Research Associate of the National Fund for Scientific Research (Belgium). † Postdoctoral Visitor of the National Fund for Scientific Research (Belgium). 2 BARNICH, GRIGORIEV, SEMIKHATOV, AND TIPUNIN