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arXiv · 2210.11154

A New Type of Lattice Gauge Theory through Self-adjoint Extensions

A. Banerjee·D. Banerjee·G. Kanwar·A. Mariani·T. Rindlisbacher·U. J. Wiese
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Abstract

A generalization of Wilsonian lattice gauge theory may be obtained by considering the possible self-adjoint extensions of the electric field operator in the Hamiltonian formalism. In the special case of 3D $\mathrm{U}(1)$ gauge theory these are parametrised by a phase $θ$, and the ordinary Wilson theory is recovered for $θ=0$. We consider the case $θ=π$, which, upon dualization, turns into a theory of staggered integer and half-integer height variables. We investigate order parameters for the breaking of the relevant symmetries, and thus study the phase diagram of the theory, which shows evidence of a broken $\mathbb{Z}_2$ symmetry in the continuum limit, in contrast to the ordinary theory.

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A. Banerjee, D. Banerjee, G. Kanwar, A. Mariani, T. Rindlisbacher, U. J. Wiese. 2022-11-25. A New Type of Lattice Gauge Theory through Self-adjoint Extensions. https://arxiv.org/abs/2210.11154

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