In the Majorana representation of a spin 1/2 we find an identity which
relates spin-spin correlators to one-particle fermionic correlators. This
should be contrasted with the straightforward approach in which two-particle
(four-fermion) correlators need to be calculated. We discuss applications to
the analysis of the dynamics of a spin coupled to a dissipative environment and
of a quantum detector performing a continuous measurement of a qubit's state
