Gravitational Properties of Quantum Bosonic Strings

In this thesis we are interested in the study of the gravitational properties of quantum bosonic strings. We start by computing the quantum energy-momentum tensor ${\hat T}^{\mu\nu}(x)$ for strings in Minkowski space-time. We perform the calculation of its expectation value for different physical string states both for open and closed bosonic strings. The states we consider are described by normalizable wave-packets in the centre of mass coordinates. Amongst our results, we find in particular that ${\hat T}^{\mu\nu}(x)$ becomes a non-local operator at the quantum level, its position appears to be smeared out by quantum fluctuations. We find that the expectation value acquires a non-zero value for both massive and massless string states. After computing $<{\hat T}^{\mu\nu}(x)>$ we proceed to calculate the gravitational field due to a quantum massless bosonic string in the framework of a weak-field approximation to Einstein's equations. We obtain a multipole expansion for the weak-field metric $h^{\mu\nu}(x)$ and present its gravitational properties, including the gravitational radiation produced by such a string. Our results are then compared to those found for classical (cosmic) strings.