Ward-Takahashi Identity and Gauge-Invariant Response Theory for Open Quantum Systems

Abstract

We derive the Ward-Takahashi identity and establish the gauge-invariant response theory for open quantum systems described by Lindbladians to show that particle-number conservation is not necessary to satisfy gauge invariance. We construct an observable which can be used to test the gauge invariance in the absence of particle-number conservation. We derive the low-energy collective modes that emerge as a consequence of gauge invariance in open quantum systems, and find that two-body loss induces diffusive modes in dissipative Bardeen-Cooper-Schrieffer (BCS) superconductivity. Possible experimental situations for testing gauge invariance in open quantum systems are also discussed.

Figures (1)

• Figure 1: Feynman diagrams for linear response to an external EM field. Here the solid and dashed lines represent the fermion and photon propagators, respectively, and $\bar{\Gamma}^{\nu}$ in the second diagram represents the full vertex including interactions and dissipation and is defined from $\bar{J}_c^{\nu}(x)=\bar{\Psi}(x)\bar{\Gamma}^{\nu}(x)\Psi(x)$.