S.Ansoldi^{1}

Dipartimento di Fisica Teorica dell'Università,

Strada Costiera 11, 34014-Trieste, Italy

Department of Physics, California State Polytechnic University

Pomona, CA 91768, USA

E.Spallucci

Dipartimento di Fisica Teorica dell'Università,

Istituto Nazionale di Fisica Nucleare, Sezione di Trieste,

Strada Costiera 11, 34014-Trieste, Italy

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.

- 1. Introduction
- 2. Functional Jacobi equation
- 3. Feynman and Jacobi path integrals
- 4. The string kernel wave equation
- 5. Computing the kernel
- 6. Conclusions
- Bibliography

*Stefano Ansoldi*
*Department of Theoretical Physics*
*University of Trieste*
*TRIESTE - ITALY*