Dynamics in hamiltonian lattice gauge theory: approaching the continuum limit with partitionings of SU(2)

Abstract In this paper, we investigate a digitised SU(2) lattice gauge theory in the Hamiltonian formalism. We use partitionings to digitise the gauge degrees of freedom and show how to define a penalty term based on finite element methods to project onto physical states of the system. Moreover, we show for a single plaquette system that in this framework the limit $$g\rightarrow 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>→</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> can be approached at constant cost.