Scattering of Quantized Dirichlet Particles

TL;DR

This paper calculates the scattering amplitude of two quantized D-particles in bosonic string theory, incorporating recoil effects and first-order acceleration corrections, providing a comprehensive and exact analysis of their quantum dynamics.

Contribution

It introduces an exact, Lorentz-invariant amplitude for D-particle scattering, computed via three methods, including recoil effects and acceleration corrections, advancing understanding of D-particle quantum interactions.

Findings

Amplitude is exact in α' and includes first-order acceleration corrections.

The amplitude is Lorentz-invariant and describes non-forward scattering with recoil.

Reproduces known forward scattering results in the infinite mass limit.

Abstract

As a step toward satisfactory understanding of the quantum dynamics of Dirichlet \break (D-) particles, the amplitude for the basic process describing the scattering of two quantized D-particles is computed in bosonic string theory. The calucluation is performed and cross-checked using three different methods, namely, (i) path integral, (ii) boundary state, and (iii) open-channel operator formalism. The analysis is exact in $\al'$ and includes the first order correction in the expansion with respect to the acceleration of the D-particles. The resultant Lorentz-invariant amplitude is capable of describing general non-forward scattering with recoil effects fully taken into account and it reproduces the known result for the special case of forward scattering in the limit of infinitely large D-particle mass. The expected form of the amplitude for the supersymmetric case is also briefly discussed.