A weak-value interpretation of the Schwinger mechanism of massless/massive pair productions

TL;DR

This paper introduces a novel weak-value-based model for pair production in electric fields, linking energy fluctuations and tunneling phenomena, and providing approximate agreement with known exponential rates.

Contribution

It proposes a new interpretation of the Schwinger mechanism using weak values, offering insights into pair production processes and their relation to tunneling phenomena.

Findings

Weak values can model energy fluctuations triggering pair production.

The model's estimates align with Landau-Zener tunneling rates.

Energy fluctuations via weak values relate to tunneling across small gaps.

Abstract

According to the Schwinger mechanism, a uniform electric field brings about pair productions in vacuum; the relationship between the production rate and the electric field is different, depending on the dimension of the system. In this paper, we make an offer of another model for the pair productions, in which weak values are incorporated: energy fluctuations trigger the pair production, and a weak value appears as the velocity of a particle there. Although our model is only available for the approximation of the pair production rates, the weak value reveals a new aspect of the pair production. Especially, within the first order, our estimation approximately agrees with the exponential decreasing rate of the Landau-Zener tunneling through the mass energy gap. In other words, such tunneling can be associated with energy fluctuations via the weak value, when the tunneling gap can be regarded as so small due to the high electric field.