Hamiltonian Truncation Framework for Gauge Theories on the Interval

In this work, we investigate gauge theories in two dimensions nonperturbatively using the Hamiltonian truncation approach. Working on a spatial interval and adopting the axial gauge, we remove all gauge field degrees of freedom and express the interacting Hamiltonian in the eigenbasis of the free Dirac theory, truncated at a finite energy. As a benchmark we analyse the Schwinger model, where our numerical spectra agree closely with the exact results from bosonization across a wide range of couplings, validating the construction of the Hamiltonian. We then generalize the formulation to nonabelian gauge groups and apply it to SU(3) gauge theory with a single massless Dirac fermion. These results demonstrate that gauge theories can be explored nonperturbatively using a truncated Hamiltonian that generates evolutions in ordinary time, offering a complementary alternative to lattice field theory.