Bound states are handled within the framework of quantum field theory.

Tim Adamo, Riccardo Gonzo. Bethe-Salpeter equation for classical gravitational bound states. 2023. https://doi.org/10.1007/jhep05(2023)088

Paper 1 uses the Bethe-Salpeter equation to describe relativistic two-body bound states in quantum field theory.

S. Ahlig, R. Alkofer. (In-) consistencies in the Relativistic Description of Excited States in the Bethe–Salpeter Equation. 1998. https://doi.org/10.1006/aphy.1999.5922

Paper 2 discusses the Bethe-Salpeter equation as the primary technique to extract bound states in relativistic quantum field theory.

Edit Mátyus, D. Ferenc, P. Jeszenszki, Á. Margócsy. The Bethe–Salpeter QED Wave Equation for Bound-State Computations of Atoms and Molecules. 2022. https://doi.org/10.1021/acsphyschemau.2c00062

Paper 3 reviews the field-theoretic Bethe-Salpeter wave equation for describing bound states in quantum electrodynamics.

Kreshchuk M, Jia S, Kirby WM, Goldstein G, Vary JP, Love PJ. Light-Front Field Theory on Current Quantum Computers.. 2021. https://doi.org/10.3390/e23050597

Paper 5 simulates bound states in relativistic quantum field theories using light-front formulations on quantum computers.

Z. Li, W. Lucha, F. Schoberl. EXACT-PROPAGATOR INSTANTANEOUS BETHE SALPETER EQUATION FOR QUARK ANTIQUARK BOUND STATES. 2005. https://doi.org/10.1142/S0217732306021001

Paper 6 uses the instantaneous approximation to the Bethe-Salpeter formalism to analyze bound states in quantum field theory.

Xiaozhao Chen, Xiaofu Lü. Development of Bethe–Salpeter theory for dealing with unstable system. 2023. https://doi.org/10.1140/epjc/s10052-023-11682-w

Paper 11 develops relativistic quantum field theory frameworks using Bethe-Salpeter equations to study bound and unstable states.