SciPost Phys. Lect. Notes 12 (2020) ·
published 17 January 2020

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In these lecture notes, we review some recent works on Hamiltonian lattice
gauge theories, that involve, in particular, tensor network methods. The
results reviewed here are tailored together in a slightly different way from
the one used in the contexts where they were first introduced, by looking at
the Gauss law from two different points of view: for the gauge field it is a
differential equation, while from the matter point of view, on the other hand,
it is a simple, explicit algebraic equation. We will review and discuss what
these two points of view allow and do not allow us to do, in terms of unitarily
gauging a purematter theory and eliminating the matter from a gauge theory,
and relate that to the construction of PEPS (Projected Entangled Pair States)
for lattice gauge theories.