Abstract
We study the Casimir effect in axion electrodynamics. A finite $\theta$-term affects the energy dispersion relation of photon if $\theta$ is time and/or space dependent. We focus on a special case with linearly inhomogeneous $\theta$ along the $z$-axis. Then we demonstrate that the Casimir force between two parallel plates perpendicular to the $z$-axis can be either attractive or repulsive, dependent on the gradient of $\theta$. We call this repulsive component in the Casimir force induced by inhomogeneous $\theta$ the anomalous Casimir effect.
Highlights
The Casimir effect [1] refers to a physical force resulting from the quantum fluctuations in the vacuum restricted by boundaries
Our present work is a natural extension to the situation with a pure spacelike bμ 1⁄4 ð0; bÞ, and as we would argue later, we discover a repulsive component of Casimir force
We model the effect of chiral medium on the Casimir force using the axion electrodynamics, that is, the U(1) electrodynamics with a topological θ term defined by the following Lagrangian density: Laxion
Summary
The Casimir effect [1] refers to a physical force resulting from the quantum fluctuations in the vacuum restricted by boundaries. Gathering substantial related efforts have given rise to a famous “no-go” theorem: the Casimir force between two bodies with reflection symmetry is always attractive [41] This no-go theorem can be circumvented in consideration that the “vacuum” in quantum field theory is not always trivial, but can have rich structures. Without breaking the reflection symmetry geometrically, a repulsive Casimir force is allowed, which indicates a specific mechanism to bypass the no-go theorem Materials exhibiting such intrinsic P and/or T symmetries breaking are familiar in condensed matter physics, and e.g., Refs. Given that a constant θðxÞ would not affect the equation of motion, we consider a linearly inhomogeneous background axion field; θðxÞ 1⁄4 bμxμ with a constant fourvector bμ This specific choice is motivated by related works about the realization of quantum anomaly in condensed matter physics as discussed in Refs.
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