Scattering of Evanescent Particles

TL;DR

This paper develops a quantum scattering theory for fields at finite distance by quantizing the Klein-Gordon field on a timelike hypercylinder, including evanescent modes, using a novel $ extalpha$-K"ahler scheme within the general boundary framework.

Contribution

It introduces a new $ extalpha$-K"ahler quantization method that incorporates evanescent modes and derives a finite-distance LSZ formula for quantum field scattering.

Findings

Established a unitary radial evolution in the quantization scheme

Derived formulas for scattering amplitudes and correlation functions at finite distance

Extended the LSZ formula to include evanescent sector contributions

Abstract

Massive Klein-Gordon theory is quantized on the timelike hypercylinder in Minkowski space. Crucially, not only the propagating, but also the evanescent sector of phase space is included, laying in this way foundations for a quantum scattering theory of fields at finite distance. To achieve this, the novel $\alpha$-K\"ahler quantization scheme is employed in the framework of general boundary quantum field theory. A potential quantization ambiguity is fixed by stringent requirements, leading to a unitary radial evolution. Formulas for building scattering amplitudes and correlation functions are exhibited. A novel LSZ formula is derived, applicable to scattering at finite distance.