Algebraic approach to time-delay data analysis for orbiting LISA

The laser phase noise is one of the dominant noises for the gravitational wave detector LISA. Since it is impossible to maintain equal distances between the spacecraft, the time-delay interferometry (TDI) techniques are used to eliminate the laser phase noise along with the optical bench noise. It has been shown for stationary case that the TDI can be formulated in a systematic manner using algebraic geometrical methods, which generate all the data combinations canceling laser phase noise. These data combinations form a module over the polynomials, formally known as first module of syzygies, in three time-delay operators corresponding to the arms of LISA. The rotation induces a difference in up and down light travel times between the spacecraft, which results in a residual laser noise. Recently, several TDI data combinations have been given to cancel the laser phase noise by taking these differences into account. In this paper, we present a rigorous formalism similar to that of stationary case, by taking different arm lengths for up and down beams, resulting in a module over polynomials in six variables. We compute the transfer functions for the six beams and obtain the response to the gravitational wave signal for the generating set of above module