Quantum Entanglement of Locally Excited States in Maxwell Theory

TL;DR

The paper analyzes how gauge-invariant local operators in four-dimensional Maxwell theory modify the (Rényi) entanglement entropy ΔS_A^(n) of a subsystem, using the replica trick to compute UV-finite excess entanglement. It demonstrates electric–magnetic duality invariance for many operator classes and shows that the late-time entanglement structure can be interpreted in terms of electromagnetic quasi-particles, with a distinct non-scalar signature arising when operators mix electric and magnetic fields in specific ways. A late-time algebra for these quasi-particles is developed, featuring left/right moving components and nontrivial E–B commutation relations that explain the observed entanglement patterns. The results illuminate how electromagnetism's internal degrees of freedom imprint unique, dimension- and operator-dependent entanglement features beyond scalar field theories, and suggest avenues for extension to general dimensions and holographic contexts.

Abstract

In 4 dimensional Maxwell gauge theory, we study the changes of (Renyi) entangle-ment entropy which are defined by subtracting the entropy for the ground state from the one for the locally excited states generated by acting with the gauge invariant local operators on the state. The changes for the operators which we consider in this paper reflect the electric-magnetic duality. The late-time value of changes can be interpreted in terms of electromagnetic quasi-particles. When the operator constructed of both electric and magnetic fields acts on the ground state, it shows that the operator acts on the late-time structure of quantum entanglement differently from free scalar fields.

Figures (4)

• Figure 1: The location of local gauge invariant operator in Minkowski spacetime.
• Figure 2: The location of local gauge invariant operator in Euclidean space.
• Figure 3: A picture of n-sheeted geometry $\Sigma_n$.
• Figure 4: The time evolution of $\Delta S^{(2)}_A$ for $E_{1}$ ($B_1$) and $E_{2, 3}$ ($B_{2, 3}$). The horizontal and vertical axes correspond to time $t$ and $\Delta S^{(2)}_A$, respectively. The red and blue lines correspond to $\Delta S^{(2)}_A$ for $E_{1}$ ($B_1$) and $E_{2, 3}$ ($B_{2, 3}$), respectively.