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Gauge-invariant rotor Hamiltonian from dual variables of 3D U(1) gauge theory

Judah F. Unmuth-Yockey*

  • Department of Physics, Syracuse University, Syracuse, New York 13244, USA

  • *jfunmuthyockey@gmail.com
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Phys. Rev. D 99, 074502 – Published 9 April, 2019

DOI: https://doi.org/10.1103/PhysRevD.99.074502

Abstract

We present a tensor formulation for free compact electrodynamics in three Euclidean dimensions and use this formulation to construct a quantum Hamiltonian in the continuous-time limit. Gauge-invariance is maintained at every step and ultimately the gauge fields are integrated out, removing all initial gauge freedom. The resulting Hamiltonian can be written as a rotor model. The energy eigenvalues for this Hamiltonian are computed using the tensor renormalization group, and are compared with perturbation theory. We find good agreement between the calculations, demonstrating a smooth passage from the statistical lattice Lagrangian description to the quantum Hamiltonian description.

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Phys. Rev. D 99, 074502– Published 9 April, 2019
  • Received 3 December 2018
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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