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

Similarly to the well-known particle-antiparticle pair production process in strong electromagnetic fields (the Schwinger effect), the matter field vacuum state can be excited by time-dependent, curved spacetime geometries. We study this process using a spacetime resolved numerical approach in the interaction picture by extending computational quantum field theory (CQFT), well-adapted to simulate the time evolution of quantum fields, to spin- 1 / 2 fermions in curved spacetime. Within this 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 Gaussian deformation of flat spacetime. Particle production is quantified by fermion-antifermion pair numbers defined with respect to the Minkowski basis of asymptotically flat spacetime. 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 postquench geometry is static and no electromagnetic field is included, this work establishes a foundation for studying particle creation in genuinely time-dependent curved spacetimes and electromagnetic backgrounds.