Application of effective theory and Grassmann variables to model compact binaries with spin - Mautner, G [UNESP] (2015)
We review how an approximation of the potential between two spin-less bodies is calculated, up to second order in the velocities, by employing eﬀective ﬁeld theory methods to model their interaction though the gravitational ﬁeld. By extending this methodology to take into account their spin degrees of free domand by describing such spin degrees of freedom in terms of Grassmannian variables, we calculate the additional terms in the potential due to spin-spin and spin-orbital interactions. Finally, we calculate the energy as a function of rotational frequency of a binary system, including the eﬀect of these spin related terms. Such results are becoming increasingly relevant in possible measurements by gravitational observatories like LIGO [1] or VIRGO [2]