Scalar field with a time-independent classical source is not trivial after all: From vacuum decay to scattering

Le résumé fourni par la source

Historically it has been believed that a time-independent classical source has no effect on the scattering of relativistic uncharged fields, in contrast with single particle quantum mechanics. In this work we show that the dynamics is not trivial. We solve exactly for the scattering amplitudes and find that a key ingredient is the production of particles from the unstable vacuum, conceptually similar to the Schwinger mechanism. We compute exactly the probabilities for the vacuum to decay in n particles. The time dependence of such probabilities displays interesting properties such as the quantum Zeno effect and, in particular, has no regime where the exponential decay law is a good approximation. We show that the trivial scattering found in the past is the by-product of the adiabatic switching of the interaction. In fact, it is not possible to switch off the interaction (adiabatically or otherwise) at distant times and recover the exact results. Finally, this nontrivial vacuum behavior is a source of particle production. We argue that such nonperturbative calculations can be phenomenologically relevant for the production processes that are suppressed at the lower orders in perturbation theory, for instance dilaton production in a medium. Published by the American Physical Society 2024

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