### Abstract

The exact relation τ =Γ between the width Γ of a resonance and the lifetime τ for the decay of this resonance could not be obtained in standard quantum theory based on the Hilbert space or Schwartz space axiom in non-relativistic physics as well as in the relativistic regime. In order to obtain the exact relation, one has to modify the Hilbert space axiom or the Schwartz space axiom and choose new boundary conditions based on the Hardy space axioms in which the space of the states and the space of the observables are described by two different Hardy spaces. As consequences of the new Hardy space axioms, one obtains, instead of the symmetric time evolution for the states and the observables, asymmetrical time evolutions for the states and observables which are described by two semi-groups. A relativistic resonance obeying the exponential time evolution can be described by a relativistic Gamow vector, which is defined as superposition of the exact out-plane wave states with a Breit-Wigner energy distribution of the width Γ.

Original language | English (US) |
---|---|

Article number | 012020 |

Journal | Journal of Physics: Conference Series |

Volume | 597 |

Issue number | 1 |

DOIs | |

State | Published - Apr 13 2015 |

Externally published | Yes |

Event | 30th International Colloquium on Group Theoretical Methods in Physics (Group30), ICGTMP 2014 - Ghent, Belgium Duration: Jul 14 2014 → Jul 18 2014 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of Physics: Conference Series*,

*597*(1), [012020]. https://doi.org/10.1088/1742-6596/597/1/012020

**Relativistic resonance and decay phenomena.** / Bui, Hai V.

Research output: Contribution to journal › Conference article

*Journal of Physics: Conference Series*, vol. 597, no. 1, 012020. https://doi.org/10.1088/1742-6596/597/1/012020

}

TY - JOUR

T1 - Relativistic resonance and decay phenomena

AU - Bui, Hai V.

PY - 2015/4/13

Y1 - 2015/4/13

N2 - The exact relation τ =Γ between the width Γ of a resonance and the lifetime τ for the decay of this resonance could not be obtained in standard quantum theory based on the Hilbert space or Schwartz space axiom in non-relativistic physics as well as in the relativistic regime. In order to obtain the exact relation, one has to modify the Hilbert space axiom or the Schwartz space axiom and choose new boundary conditions based on the Hardy space axioms in which the space of the states and the space of the observables are described by two different Hardy spaces. As consequences of the new Hardy space axioms, one obtains, instead of the symmetric time evolution for the states and the observables, asymmetrical time evolutions for the states and observables which are described by two semi-groups. A relativistic resonance obeying the exponential time evolution can be described by a relativistic Gamow vector, which is defined as superposition of the exact out-plane wave states with a Breit-Wigner energy distribution of the width Γ.

AB - The exact relation τ =Γ between the width Γ of a resonance and the lifetime τ for the decay of this resonance could not be obtained in standard quantum theory based on the Hilbert space or Schwartz space axiom in non-relativistic physics as well as in the relativistic regime. In order to obtain the exact relation, one has to modify the Hilbert space axiom or the Schwartz space axiom and choose new boundary conditions based on the Hardy space axioms in which the space of the states and the space of the observables are described by two different Hardy spaces. As consequences of the new Hardy space axioms, one obtains, instead of the symmetric time evolution for the states and the observables, asymmetrical time evolutions for the states and observables which are described by two semi-groups. A relativistic resonance obeying the exponential time evolution can be described by a relativistic Gamow vector, which is defined as superposition of the exact out-plane wave states with a Breit-Wigner energy distribution of the width Γ.

UR - http://www.scopus.com/inward/record.url?scp=84928034590&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84928034590&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/597/1/012020

DO - 10.1088/1742-6596/597/1/012020

M3 - Conference article

AN - SCOPUS:84928034590

VL - 597

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012020

ER -