FIRST QUANTIZED NONCRITICAL RELATIVISTIC POLYAKOV STRING

The first quantization of the relativistic Brink-DiVecchia-Howe-Polyak ov (BDHP) string in the range 1 < d < 25 is considered. It is shown th at using the Polyakov sum over bordered surfaces in the Feynman path i ntegral quantization scheme one gets a consistent quantum mechanics of relativistic one-dimensional extended objects in the range 1 < d < 25 . In particular the BDHP string propagator is exactly calculated for a rbitrary initial and final string configurations and the Hilbert space of physical states of noncritical BDHP string is explicitly construct ed. The resulting. theory is equivalent to the Fairlie-Chodos-Thorn ma ssive string model. In contrast to the conventional conformal field th eory approach to noncritical string and random surfaces in the Euclide an target space the path integral formulation of the Fairlie-Chodos-Th orn string obtained in this paper does not rely on the principle of co nformal invariance. Some consequences of this feature for constructing a consistent relativistic string theory based on the ''splitting-join ing'' interaction are discussed.