Gauge choices and Entanglement Entropy of two dimensional lattice gauge fields

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In this paper, we explore the question of how different gauge choices in a gauge theory affect the tensor product structure of the Hilbert space in configuration space.

• In particular, we study the Coulomb gauge and observe that the naive gauge potential degrees of freedom cease to be local operators as soon as we impose the Dirac brackets.
• We construct new local set of operators and compute the entanglement entropy according to this algebra in $2+1$ dimensions.
• We find that our proposal would lead to an entanglement entropy that behave very similar to a single scalar degree of freedom if we do not include further centers, but approaches that of a gauge field if we include non-trivial centers.