Pairs Emission in a Uniform Background Field: an Algebraic Approach

TL;DR

This paper introduces an algebraic framework for analyzing pair emission and absorption in uniform background fields, revealing an SU(2) algebra structure and recovering the Schwinger formula for pair production.

Contribution

It develops a novel algebraic approach that unifies pair processes and demonstrates the SU(2) algebra structure underlying pair operators in external fields.

Findings

Pairs operators form an SU(2) algebra.

The Schwinger formula is derived within this algebraic framework.

The approach provides a consistent method for pair production analysis.

Abstract

A fully algebraic general approach is developed to treat the pairs emission and absorption in the presence of some uniform external background field. In particular, it is shown that the pairs production and annihilation operators, together with the pairs number operator, do actually fulfill the SU(2) functional Lie algebra. As an example of application, the celebrated Schwinger formula is consistently and nicely recovered, within this novel approach, for a Dirac spinor field in the presence of a constant and homogeneous electric field in four spacetime dimensions.