String Propagator: a Loop Space Representation

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

A.Aurilia²
Department of Physics, California State Polytechnic University
Pomona, CA 91768, USA

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

Abstract:

The string quantum kernel is normally written as a functional sum over the string coordinates and the world-sheet metrics. As an alternative to this quantum field-inspired approach, we study the closed bosonic string propagation amplitude in the functional space of loop configurations. This functional theory is based entirely on the Jacobi variational formulation of quantum mechanics, without the use of a lattice approximation. The corresponding Feynman path integral is weighed by a string action which is a reparametrization invariant version of the Schild action. We show that this path integral formulation is equivalent to a functional ``Schrödinger'' equation defined in loop-space. Finally, for a free string, we show that the path integral and the functional wave equation are exactly solvable.