Two-particle truncation of Pauli–Villars-regulated Yukawa theory∗

Department of Physics, Southern Methodist University, Dallas, TX 75275 (Dated: September 4, 2002) Abstract We obtain analytic, nonperturbative, approximate solutions of Yukawa theory in the one-fermion sector using light-front quantization. The theory is regulated in the ultraviolet by the introduction of heavy Pauli–Villars scalar and fermion fields, each with negative norm. In order to obtain a directly soluble problem, fermion-pair creation and annihilation are neglected, and the number of bosonic constituents is limited to one of either type. We discuss some of the features of the wave function of the eigensolution, including its endpoint behavior and spin and orbital angular momentum content. The limit of infinite Pauli–Villars mass receives special scrutiny.