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

Abstract

Relativistic resonances and decaying states are described by representations of Poincaré 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 Poincaré transformations into the forward light cone.

57 pages, 6 figures

References in corpus (6)

• A Pedestrian Introduction to Gamow Vectors
• Radiative Corrections to W and Quark Propagators in the Resonance Region
• Time Asymmetric Quantum Physics
• Gamow-Jordan Vectors and Non-Reducible Density Operators from Higher Order S-Matrix Poles
• Relativistic Partial Wave Analysis Using the Velocity Basis of the Poincare Group
• Semigroup Representations of the Poincare Group and Relativistic Gamow Vectors

Cited by in corpus (11)

• Relativistic resonances: Their masses, widths, lifetimes, superposition, and causal evolution
• The Friedrichs Model and its use in resonance phenomena
• Basis States for Relativistic, Dynamically-Entangled Particles
• Time Asymmetric Quantum Theory - III. Decaying States and the Causal Poincare Semigroup
• Time Asymmetric Quantum Mechanics
• Clebsch-Gordan Coefficients for the Extended Quantum-Mechanical Poincaré Group and Angular Correlations of Decay Products
• Point-form dynamics of quasistable states
• Poincare Semigroup Symmetry as an Emergent Property of Unstable Systems
• Observations on Unstable Quantons, Hyperplane Dependence and Quantum Fields
• Analysis of resonance production using relativistic Gamow vectors
• Groups, Special Functions and Rigged Hilbert Spaces