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

Similarly to the well-known phenomenon of particle / anti-particle pair production in strong electromagnetic fields (the Schwinger effect), the naïve 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.

💡 Research Summary

This paper presents a numerical study of fermion–antifermion pair creation induced solely by a localized curvature perturbation in a 1+1‑dimensional spacetime. Building on the Computational Quantum Field Theory (CQFT) framework that has previously been applied to strong‑field QED problems, the authors extend the method to curved backgrounds by incorporating the vierbein formalism and the spin connection into a covariant Dirac equation. They derive a Hermitian Hamiltonian that contains both the kinetic term and curvature‑dependent interaction terms, and they implement real‑time evolution using a split‑operator scheme that preserves unitarity and avoids fermion‑doubling on the lattice.

The spacetime geometry is constructed by adding a smooth Gaussian “curvature bump” to an otherwise flat Minkowski metric. The bump is characterized by a peak amplitude ε and a spatial width σ, and it is switched on abruptly at t = 0, after which the geometry settles into a static configuration. The initial state is the Minkowski vacuum, defined with respect to the asymptotic flat region. By evolving the field operator with the unitary time‑evolution operator and re‑expanding it in the free‑Minkowski mode basis, the authors obtain time‑dependent annihilation and creation operators for particles and antiparticles. From these, they compute momentum‑resolved occupation numbers ⟨0|b†p(t) bp(t)|0⟩ and ⟨0|d†p(t) dp(t)|0⟩, which serve as proxies for the number of created pairs.

The numerical results show that both the strength (ε) and the spatial extent (σ) of the curvature bump control the pair‑production rate. Larger ε or broader σ lead to higher occupation numbers across a wider range of momenta. The creation process is sharply peaked in time, reflecting a tunnelling‑like burst when the curvature is switched on, and a residual steady‑state density persists after the geometry becomes static. These findings support the interpretation that a localized curvature acts as an effective potential analogous to a strong electric field in the Schwinger effect, driving vacuum decay without any electromagnetic background.

A significant portion of the discussion addresses the ambiguity of particle number at intermediate times. Since the definition relies on a chosen mode basis (here the asymptotic Minkowski modes), the computed occupation numbers are not invariant under different observer choices and should be regarded as “vacuum excitation” rather than directly observable particle yields. The authors argue that meaningful particle counts are only unambiguous in regions where the curvature vanishes and free‑particle notions are well defined.

The paper acknowledges several limitations: the study is restricted to 1+1 dimensions, the post‑quench geometry is static, and no electromagnetic fields are present. Nevertheless, the presented framework is readily generalizable to higher dimensions, time‑dependent metrics, and combined gravitational‑electromagnetic backgrounds. The authors suggest future applications to Hawking‑like radiation, cosmological particle production during inflation, and analogue gravity platforms such as strained graphene, where effective metrics can be engineered experimentally. Overall, the work establishes a versatile, non‑perturbative computational tool for exploring quantum field phenomena in arbitrary curved spacetimes.