Vacuum polarisation induced coupling between Maxwell and Kalb-Ramond Fields

TL;DR

This paper calculates the gauge-invariant vacuum polarization effects for fermions in constant Maxwell and Kalb-Ramond fields, revealing an effective coupling in the weak field limit that links these fields through a specific squared interaction.

Contribution

It generalizes Schwinger's formalism to include Kalb-Ramond fields, providing explicit vacuum polarization expressions and identifying a novel Maxwell-Kalb-Ramond coupling.

Findings

Derived explicit vacuum polarization induced effective Lagrangian.

Identified a $( ilde{H}. ilde{F})^2$ coupling in the weak field limit.

Extended gauge invariance formalism to include Kalb-Ramond fields.

Abstract

We present here a manifestly gauge invariant calculation of vacuum polarization to fermions in the presence of a constant Maxwell and a constant Kalb-Ramond field in four dimensions. The formalism is a generalisation of the one used by Schwinger in his famous paper on gauge invariance and vacuum polarization. We get an explicit expression for the vacuum polarization induced effective Lagrangian for a constant Maxwell field interacting with a constant Kalb-Ramond field. In the weak field limit we get the coupling between the Maxwell field and the Kalb-Ramond field to be $(\tilde{H}.\tilde{F})^2$, where ${\tilde H}_{\mu}= {1\over {3!}}\epsilon_{\mu\alpha\beta\lambda}H^{\alpha\beta\lambda}$ and $\tilde F$ is the dual of $F_{\mu\nu}$.