Quantum bosonic string energy-momentum tensor in Minkowski space-time

The quantum energy-momentum tensor T̂ (x) is computed for strings in Minkowski space-time. We compute its expectation value for different physical string states both for open and closed bosonic strings. The states considered are described by normalizable wave-packets in the center of mass coordinates. We find in particular that T̂ (x) is finite which could imply that the classical divergence that occurs in string theory as we approach the string position is removed at the quantum level as the string position is smeared out by quantum fluctuations. For massive string states the expectation value of T̂ (x) vanishes at leading order (genus zero). For massless string states it has a non-vanishing value which we explicitly compute and analyze for both spherically and cylindrically symmetric wave packets. The energymomentum tensor components propagate outwards as a massless lump peaked at r = t. 1 Laboratoire Associé au CNRS UA 280.