Relativistic Resonances, Relativistic Gamow Vectors and Representations of the Poincare' Semigroup

TL;DR

This paper develops a framework for relativistic Gamow vectors derived from the S-matrix resonance poles, providing a time-asymmetric quantum description of quasistable particles like the Z-boson within the Poincare' semigroup representation.

Contribution

It introduces a novel construction of relativistic Gamow vectors from the S-matrix resonance poles, establishing their role as irreducible representations of the Poincare' semigroup with time asymmetry.

Findings

Relativistic Gamow vectors are obtained from the S-matrix resonance pole.

They form irreducible representations of the Poincare' semigroup.

They exhibit a semigroup time evolution into the forward light cone.

Abstract

The foundations of time asymmetric quantum theory are reviewed and are applied to the construction of relativistic Gamow vectors. Relativistic Gamow vectors are obtained from the resonance pole of the S-matrix and furnish an irreducible representation of the Poincare' semigroup. They have all the properties needed to represent relativistic quasistable particles and can be used to fix the definition of mass and width of relativistic resonances like the Z-boson. Most remarkably, they have only a semigroup time evolution into the forward light cone---expressing time asymmetry on the microphysical level.