Time-delay interferometry and the relativistic treatment of LISA optical links

In order to attain the requisite sensitivity for LISA - a joint space mission of the ESA and NASA- the laser frequency noise must be suppressed below the secondary noises such as the optical path noise, acceleration noise etc. By combining six appropriately time-delayed data streams containing fractional Doppler shifts - a technique called time delay interferometry (TDI) - the laser frequency noise may be adequately suppressed. Here we investigate the problem of TDI in the general case of unequal up-down links and also include the effect of the Earth on the spacecraft and the optical links. We show that there are symmetries in the physics which can be successfully used to simplify the algebra of the TDI. We finally give the example of the first generation modified Sagnac observable in which the laser frequency noise is suppressed because of the symmetries