TDI-1: time-delay interferometry without delays

The space-based gravitational-wave observatory LISA relies on a form of synthetic interferometry(time-delay interferometry, or TDI) where the otherwise overwhelming laser phase noise is canceledby linear combinations of appropriately delayed phase measurements. These observables grow inlength and complexity as the realistic features of the LISA orbits are taken into account. In thispaper we outline an implicit formulation of TDI where we write the LISA likelihood directly interms of the basic phase measurements, and we marginalize over the laser phase noises in thelimit of innite laser-noise variance. Equivalently, we rely on TDI observables that are denednumerically (rather than algebraically) from a discrete-lter representation of the laser propagationdelays. Our method generalizes to any time dependence of the armlengths; it simplies the modelingof gravitational-wave signals; and it allows a straightforward treatment of data gaps and missingmeasurements.