Abstract
Schwinger pair production is analyzed in a BPST instanton background and in its SL$(2,\mathbb{C})$ complex extension for complex scalar particles. A non-Abelian extension of the worldline instanton method is utilized, wherein Wong's equations in a coherent state picture adopted for SL$(2,\mathbb{C})$ are solved in Euclidean spacetime. While pair production is not predicted in the BPST instanton, a complex extension of the BPST instanton, existing as parallel fields in Minkowski spacetime, is shown to decay via the Schwinger effect.
Highlights
The quantum field theoretic (QFT) vacuum in a strong electric field is thought unstable against the production of particle anti-particle pairs in what is known as the Schwinger mechanism [1]
Schwinger pair production has been analyzed in the topological BPST instanton (YMI), and due to the Hermiticity of its construction, no vacuum decay via the Schwinger effect was found as anticipated
As an anomaly cancellation is found for Abelian homogeneous fields, it is likewise anticipated that a non-Abelian field configuration with Chern-Pontryagin density should be present and decay via the Schwinger effect
Summary
The quantum field theoretic (QFT) vacuum in a strong electric field is thought unstable against the production of particle anti-particle pairs in what is known as the Schwinger mechanism [1]. The case of massless fermions under a isotropic and homogeneous SU(2) gauge field background with a nonvanishing Chern-Pontryagin density leading to the chiral anomaly via the Schwinger effect was explored in [9]. To arrive at Wong’s equations we employ a coherent state formalism [22] on the Wilson loop, converting the propertime ordered matrix weighted exponential into a path integral over the Haar measure. This process is known for the non-Abelian Stokes theorem [23,24] as well as for the chiral kinetic theory [25], with non-Abelian degrees of freedom [26]. In this paper we consider SUð2ÞC, extending the WI formalism to explore non-Abelian topologically nontrivial fields, and through analytical continuation we parametrize the effective action.
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