Observer dependence of bubble nucleation and Schwinger pair production

TL;DR

This paper investigates how different observers perceive bubble nucleation and Schwinger pair production in a constant electric field, demonstrating Lorentz invariance of the quantum state and observer-dependent particle detection.

Contribution

It introduces a model detector to analyze observer dependence in pair production, showing the Lorentz invariance of the in-vacuum and the observer-specific nucleation at rest in the detector frame.

Findings

Quantum state is Lorentz invariant despite gauge choices.

All observers see nucleation at rest in their frame.

In-vacuum contains an infinite density of particles, which can be mitigated by Lorentz-breaking conditions.

Abstract

Pair production in a constant electric field is closely analogous to bubble nucleation in a false vacuum. The classical trajectories of the pairs are Lorentz invariant, but it appears that this invariance should be broken by the nucleation process. Here, we use a model detector, consisting of other particles interacting with the pairs, to investigate how pair production is seen by different Lorentzian observers. We focus on the idealized situation where a constant external electric field is present for an infinitely long time, and we consider the in-vacuum state for a charged scalar field that describes the nucleating pairs. The in-vacuum is defined in terms of modes which are positive frequency in the remote past. Even though the construction uses a particular reference frame and a gauge where the vector potential is time dependent, we show explicitly that the resulting quantum state is Lorentz invariant. We then introduce a "detector" particle which interacts with the nucleated pairs, and show that all Lorentzian observers will see the particles and antiparticles nucleating preferentially at rest in the detector's rest frame. Similar conclusions are expected to apply to bubble nucleation in a sufficiently long lived vacuum. We also comment on certain unphysical aspects of the Lorentz invariant in-vacuum, associated with the fact that it contains an infinite density of particles. This can be easily remedied by considering Lorentz breaking initial conditions.