Relativistic bound-state models with quasifree constituent motion

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Abstract
Prototype relativistic bound-state models are considered which avoid normalization and spectral problems usually associated with such models. A novel approach based on the use of hyperboloidal coordinates allows us to take advantage of an attractive angular-momentum-like term in □ to obtain kinematic binding in the timelike region of the relative-coordinate Minkowski space. Besides allowing for a type of free quark behavior within the bound state this feature eliminates the spectral problem. We develop a half-space harmonic-oscillator model with a positive-definite, almost linear spectrum.