Time Asymmetric Quantum Theory - III. Decaying States and the Causal Poincare Semigroup

Abstract

A relativistic resonance which was defined by a pole of the $S$-matrix, or by a relativistic Breit-Wigner line shape, is represented by a generalized state vector (ket) which can be obtained by analytic extension of the relativistic Lippmann-Schwinger kets. These Gamow kets span an irreducible representation space for Poincaré transformations which, similar to the Wigner representations for stable particles, are characterized by spin (angular momentum of the partial wave amplitude) and complex mass (position of the resonance pole). The Poincaré transformations of the Gamow kets, as well as of the Lippmann-Schwinger plane wave scattering states, form only a semigroup of Poincaré transformations into the forward light cone. Their transformation properties are derived. From these one obtains an unambiguous definition of resonance mass and width for relativistic resonances. The physical interpretation of these transformations for the Born probabilities and the problem of causality in relativistic quantum physics is discussed.

arXiv comment49 pages, 1 figure

References in corpus (5)

• Time Asymmetric Quantum Physics
• On the Mass and Width of the Z-boson and Other Relativistic Quasistable Particles
• Time Asymmetric Quantum Theory - II. Relativistic Resonances from S-Matrix Poles
• Relativistic Partial Wave Analysis Using the Velocity Basis of the Poincare Group
• Irreversible Quantum Mechanics in the Neutral K-System

Cited by in corpus (8)

• Relativistic resonances: Their masses, widths, lifetimes, superposition, and causal evolution
• Basis States for Relativistic, Dynamically-Entangled Particles
• 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
• Groups, Special Functions and Rigged Hilbert Spaces
• Analysis of resonance production using relativistic Gamow vectors