String representation of quantum loops

We recover a general representation for the quantum state of a relativistic closed line (loop) in terms of string degrees of freedom. The general form of the loop functional splits into the product of the Eguchi functional, e ncoding the holographic quantum dynamics, limes the Polyakov path integral. taking into account the full bulk dynamics, times a loop effective action, which is needed to renormalize boundary ultraviolet divergences. The Polya kov string action is derived as an effective action from a phase space, cov ariant, Schild action, by functionally integrating out the worldsheet coord inates. The area coordinates description of the boundary quantum dynamics, is shown to be induced by the 'zero mode' of the bulk quantum fluctuations. Finally, we briefly comment about a 'unified, fully covariant' description of points, loops and strings in terms of matrix coordinates.