MASS AND ENERGY-MOMENTUM TENSOR OF QUANTUM STRINGS IN GRAVITATIONAL SHOCK-WAVES

We investigate at the quantum level the nonlinear transformation relating the string operators (zero modes and oscillators) and Fock space states before and after the collision with gravitational shock waves. This throws light on the rôle of the space–time geometry in this problem. We do all the treatment for a general shock wave space–time of any localized source. We compute the exact expectation values of the total number (N) and mass (M²) operators and show that they are finite, which generalize our previous results in the Aichelburg–Sexl geometry. We study the energy-momentum tensor of the string and compute the exact expectation values of all its components. We analyze vacuum polarization and quadratic fluctuations. All these physical magnitudes are finite. We express all of them in terms of exact integral representations in which the role of the real pole singularities characteristic of the tree level string spectrum (real mass resonances) are clearly exhibited. The presence of such poles is not at all related to the structure of the space–time geometry (which may or may not be singular).