BRST FIELD-THEORIES FOR A QUANTUM LORENTZ PARTICLE

From the study of string field theory, first quantized BRST symmetry is known to be a guiding principle in constructing field theories. We construct the first quantized BRST charge Q(B) for a quantum Lorentz particle which is characterized by the constraints which are expressed in terms of (inhomogeneous) Lorentz generators. It is shown that the BRST cohomology of this system includes only the field strengths and not the fundamental gauge fields with nontrivial norms. By using this BRST charge, we obtain the field theory Lagrangian via the integral PSI-Q(B)-PSI construction, which leads to field equations for fields with arbitrary spin. However, this action cannot be used to derive a second quantized theory except for Dirac fields. For antisymmetric tensor fields, we can get the correct second quantized theories if we introduce extra conditions.