Loop, String, and Hadron Dynamics in SU(2) Hamiltonian Lattice Gauge Theories*

We present a reformulation of an SU(2) Hamiltonian lattice gauge theory---a loop-string-hadron (LSH) formulation---that characterizes dynamics directly in terms of its loop, string, and hadronic degrees of freedom, while alleviating several disadvantages of quantumly simulating the Kogut-Susskind formulation. This LSH formulation, derived from Schwinger bosons, transcends the local loop formulation of ($d$+1)-dimensional lattice gauge theories by incorporating staggered quarks, furnishing an algebra of gauge-singlet operators, and succinctly encoding the dynamics among states having Gauss’s law built in to them. LSH operators are factored into explicit products of ``normalized'' ladder operators and diagonal matrices, priming them for applications in classical or quantum algorithms. Self-contained translations of the Hamiltonian are given up to $d$=3.