We describe a family of twisted partition functions for the relativistic
spinning particle models. For suitable choices of fugacities this computes a
refined Euler characteristics that counts the dimension of the physical states
for arbitrary picture and, furthermore, encodes the complete BV-spectrum of the
effective space-time gauge theory originating from this model upon second
quantization. The relation between twisted world-line partition functions and
the spectrum of the space-time theory is most easily seen on-shell but we will
give an off-shell description as well. Finally we discuss the construction of a
space-time action in terms of the world-line fields in analogy to string field
theory.Comment: 31 pages