Computational quantum field theory for fermion pair creation in 2-dimensional curved spacetimes

TL;DR

This paper extends computational quantum field theory to spin-1/2 fermions in curved spacetime, enabling numerical study of vacuum excitation and fermion pair creation due to spacetime curvature changes, with potential for future dynamic and electromagnetic scenarios.

Contribution

It develops a numerical framework for simulating fermionic quantum fields in curved spacetime, specifically incorporating spin-1/2 particles, and applies it to analyze vacuum excitation caused by a localized curvature bump.

Findings

Vacuum excitation depends on curvature strength and extent.

Numerical method successfully models fermion pair creation in curved backgrounds.

Framework lays groundwork for future studies in dynamic spacetimes and electromagnetic fields.

Abstract

Similarly to the well-known phenomenon of particle / anti-particle pair production in strong electromagnetic fields (the Schwinger effect), the na\"ive matter field vacuum state can be excited by time-dependent, curved spacetime geometries. This gravitational pair creation corresponds to tunnelling out of a false vacuum. In this work, we study this non-perturbative process using a spacetime resolved numerical approach in the interaction picture. To achieve this, we extend the framework of Computational Quantum Field Theory (CQFT), which allows for efficient numerical time evolution of quantum fields, to spin-$1/2$ fermions in curved spacetime. Using this extended framework, we investigate vacuum excitation of a Dirac field induced by a spacetime-curvature quench. In particular, we evolve the fermionic Minkowski vacuum in a $1\!+\!1$-dimensional idealized curved spacetime characterized by a localized ``curvature bump'' generated by a smooth, localized Gaussian deformation of flat spacetime. Vacuum excitation is quantified by computing the fermion--antifermion pair numbers defined with respect to the basis corresponding to flat-spacetime (Minkowski) which is the asymptotic metric corresponding to an observor at infinity. We analyze how the excitation depends on the strength and spatial extent of the curvature deformation and discuss the numerical implementation of CQFT in curved backgrounds. While the post-quench geometry considered here is static and no electromagnetic field is included, the present work establishes a foundation for future investigations of particle creation in genuinely time-dependent curved spacetimes and in the presence of electromagnetic backgrounds.