String Representation of Quantum Loops

S.Ansoldi¹
Dipartimento di Fisica Teorica dell'Università,
Strada Costiera 11, 34014-Trieste, Italy

C.Castro²
Center for Theoretical Studies of Physical Systems,
Clark Atlanta University,
Atlanta, Georgia 30314 USA

E.Spallucci³
Dipartimento di Fisica Teorica dell'Università,
Istituto Nazionale di Fisica Nucleare, Sezione di Trieste,
Strada Costiera 11, 34014-Trieste, Italy

Abstract:

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, encoding the holographic quantum dynamics, times 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 Polyakov string action is derived as an effective action from a phase space, covariant, Schild action, by functionally integrating out the world-sheet coordinates. 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.