CLASSICAL AND QUANTUM STRINGS IN PLANE WAVES, SHOCK WAVES AND SPACE–TIME SINGULARITIES: SYNTHESIS AND NEW RESULTS

Abstract

Key issues and essential features of classical and quantum strings in gravitational plane waves, shock waves and space–time singularities are synthetically understood. This includes the string mass and mode number excitations, energy–momentum tensor, scattering amplitudes, vacuum polarization and wave-string polarization effect. The role of the real pole singularities characteristic of the tree level string spectrum (real mass resonances) and that of the space–time singularities is clearly exhibited. This throws light on the issue of singularities in string theory which can be thus classified and fully physically characterized in two different sets: strong singularities (poles of order ≥ 2, and black holes) where the string motion is collective and nonoscillating in time, outgoing states and scattering sector do not appear, the string does not cross the singularities; and weak singularities (poles of order < 2, (Dirac δ belongs to this class) and conic/orbifold singularities) where the whole string motion is oscillatory in time, outgoing and scattering states exist, and the string crosses the singularities. Common features of strings in singular wave backgrounds and in inflationary backgrounds are explicitly exhibited. The string dynamics and the scattering/excitation through the singularities (whatever their kind: strong or weak) is fully physically consistent and meaningful.