The Quantization of the Spacetime Geometry Generated by Planckian Energy Particles

Details The Quantization of the Spacetime Geometry Generated by Planckian Energy Particles The Quantization of the Spacetime Geometry Generated by Planckian Energy Particles

1993-03-02

arxiv.org/abs/gr-qc/9303004v2

in Cosmology and Particle Physics, V.de Sabbata and Tso-Hsiu Eds, Kluwer Ac. Publ., Dordrecht (1994), Vol. C427, pp 193-199

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, Plain TEX

Scientific paper

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).

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