Preliminary results on a canonical formulation of general relativity based on an analogy with the string model of elementary particles are presented. Rather than the metric components, the basic fields of the formalism are taken to be the functions describing the embedding of four dimensional spacetime in a ten or possibly higher dimensional manifold. So far, the main drawback of the formalism is that the generator of normal deformations ("fourth constraint") cannot be written down in closed form. The present approach is compared and contrasted with the usual one and with the canonical description of the relativistic string.

General Relativity \`a la string: a progress report

Solution of the relativistic string problem

The bosonic string in D-dimensional Minkowski space–time is quantized in a static gauge. It is shown that the system can be described by D − 1 massless free fields constrained on the surface Lm = 0, for m ≠ 0, where Lm are the generators of conformal transformations. The free fields are quantized and the physical states are selected by the conditions Lm|Ψph〉 = 0, for m > 0. The Poincare group generators on the physical Hilbert space are constructed and the critical dimension D = 26 is recovered from the commutation relations of the boost operators. The equivalence with the covariant quantization is established. A possible generalization to the AdS string dynamics is discussed.

Bosonic string quantization in a static gauge

The bosonic string in D dimensional Minkowski space-time is quantized in static gauge. It is shown that the system can be described by D-1 massless free fields constrained on the surface L_m = 0, for m \neq 0, where L_m are the generators of conformal transformations. The free fields are quantized and the physical states are selected by the conditions L_m|phys>=0, for m>0. The Poincar\'e group generators on the physical Hilbert space are constructed and the critical dimension D=26 is recovered from the commutation relations of the boost operators. The equivalence with the covariant quantization is established. A possible generalization to the AdS string dynamics is discussed.

G. Ponzano

Papers

The quantization of a massless relativistic string in a time-like gauge