Evanescent Particles

TL;DR

This paper develops a novel quantization approach for evanescent particles in Klein-Gordon theory on timelike hyperplanes, revealing new quantum states and boundary effects, including a Casimir state with particle pair creation.

Contribution

It introduces the $ extalpha$-K"ahler quantization method for evanescent sectors and analyzes non-unitary evolution and boundary conditions in this context.

Findings

Quantization of evanescent sector with a correct vacuum

Non-unitary evolution between hyperplanes due to quantization ambiguity

Identification of the Casimir state as an alternative vacuum with particle pairs

Abstract

Massive Klein-Gordon theory is quantized on a timelike hyperplane in Minkowski space using the framework of general boundary quantum field theory. In contrast to previous work, not only the propagating sector of the phase space is quantized, but also the evanescent sector, with the correct physical vacuum. This yields for the first time a description of the quanta of the evanescent field alone. The key tool is the novel $\alpha$-K\"ahler quantization prescription based on a $*$-twisted observable algebra. The spatial evolution of states between timelike hyperplanes is established and turns out to be non-unitary if different choices are made for the quantization ambiguity for initial and final hyperplane. Nevertheless, a consistent notion of transition probability is established also in the non-unitary case, thanks to the use of the positive formalism. Finally, it is shown how a conducting boundary condition on the timelike hyperplane gives rise to what we call the Casimir state. This is a pseudo-state which can be interpreted as an alternative vacuum and which gives rise to a sea of particle pairs even in this static case.