Time Asymmetric Quantum Theory - II. Relativistic Resonances from S-Matrix Poles

Details Time Asymmetric Quantum Theory - II. Relativistic Resonances from S-Matrix Poles Time Asymmetric Quantum Theory - II. Relativistic Resonances from S-Matrix Poles

2002-12-22

arxiv.org/abs/hep-th/0212280v1

Fortsch.Phys. 51 (2003) 569-603

Physics

High Energy Physics

High Energy Physics - Theory

57 pages, 6 figures

Scientific paper

10.1002/prop.200310074

Relativistic resonances and decaying states are described by representations of Poincar\'e transformations, similar to Wigner's definition of stable particles. To associate decaying state vectors to resonance poles of the $S$-matrix, the conventional Hilbert space assumption (or asymptotic completeness) is replaced by a new hypothesis that associates different dense Hardy subspaces to the in- and out-scattering states. Then one can separate the scattering amplitude into a background amplitude and one or several ``relativistic Breit-Wigner'' amplitudes, which represent the resonances per se. These Breit-Wigner amplitudes have a precisely defined lineshape and are associated to exponentially decaying Gamow vectors which furnish the irreducible representation spaces of causal Poincar\'e transformations into the forward light cone.

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