Bakamjian–Thomas construction for quasistable states

Abstract

As is evident from the multiple values listed in the particle data table for the mass and width of resonances, such as Z°, Δ and ρ, defining these resonance parameters uniquely and unambiguously remains an open problem. This problem is ultimately rooted in the absence of a state vector description of a resonance that has definite properties under spacetime transformations. We show that there exist irreducible representations of the causal Poincaré semigroup that provide such a state vector description to resonances, leading to well-defined mass and width parameters. Generated by an interaction-incorporating Poincaré algebra and characterized by the complex S-matrix pole position and spin of the resonance, these representations synthesize the Bakamjian–Thomas construction of relativistic interactions and the S-matrix description of resonances.