Analysis of resonance production using relativistic Gamow vectors

TL;DR

This paper presents a consistent framework for calculating resonance production amplitudes using relativistic Gamow vectors, integrating them with stable particle kinematics within the Dirac formalism.

Contribution

It introduces a novel approach to incorporate relativistic Gamow vectors into the standard quantum formalism for resonance analysis.

Findings

Demonstrates compatibility of relativistic Gamow vectors with stable particle kinematics

Provides a consistent calculation framework for resonance amplitudes

Bridges the gap between complex mass states and conventional quantum mechanics

Abstract

The calculation of an amplitude involving resonance production is presented. This calculation employs for the resonance state a relativistic Gamow vector. It is used for investigating the question of compatibility of the relativistic Gamow vectors kinematics, defined by real 4-velocities and complex mass, with the stable particle kinematics; or in other words, the integration of the Gamow vectors with the conventional Dirac bra-ket formalism. The calculation demonstrates a consistent framework comprising stable and Gamow vectors.