Hamiltonian Lattice Formulation for Abelian and Non-Abelian Gauge Theories

Xiaojun Yao, PhD

Lattice formulation is a non-perturbative tool to study gauge theories. The Euclidean path integral approach has been widely used to study static properties of these theories, including hadron spectrum, hadron structure, and thermodynamic quantities at equilibrium. Due to the sign problem, it is challenging to extract real-time physical quantities via the Euclidean lattice approach. With the recent developments in quantum technology, the Hamiltonian lattice approach has attracted a great deal of interest and is being investigated from many different perspectives. In this talk, I will review the Kogut-Susskind Hamiltonian setup and discuss applications to SU(2) and SU(3) lattice gauge theories. If time permits, I will also discuss an alternative setup for QED in the Coulomb gauge, which leads to efficient circuit construction and gate count.