Constraints, Center-of-Masses and Quantization for Relativistically Structured Systems: The Bilocal Case

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Abstract
Based on general Hamiltonian formalism the algebraic structure of bilocal theory is elucidated. This is much more specific than the general Poincaré algebra, being governed by the existence of geometrical center-of-mass and the occurrence of constraints in the original covariant formalism. The boost transformation bringing the internal variables to center-of-mass rest frame isolated the constraints and brings about the definition of canonical but non-covariant center-of-mass. This enables us the quantization of theory which is non-covariant but free from subsidiary condition. This quantization and the original covariant quantization accompanying subsidiary condition are shown to be connected by a definite unitary transformation. Applications of theory to specified bilocal models are made, leading to detailed analysis.

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