The Quantization of the Spacetime Geometry Generated by Planckian Energy Particles

Abstract

We study the quantization of the curved spacetime created by ultrarelativistic particles at Planckian energies. We consider a minisuperspace model based on the classical shock wave metric generated by these particles, and for which the Wheeler - De Witt equation is solved exactly. The wave function of the geometry is a Bessel function whose argument is the classical action. This allows us to describe not only the semiclassical regime $(S\to\infty),$ but also the strong quantum regime $(S\to0).$ We analyze the interaction with a scalar field $\phi$ and apply the third quantization formalism to it. The quantum gravity effects make the system to evolve from a highly curved semiclassical geometry (a gravitational wave metric) into a strongly quantum state represented by a weakly curved geometry (essentially flat spacetime).