TY - JOUR

T1 - Description of Unstable Systems in Relativistic Quantum Mechanics in the Lax-Phillips Theory

AU - Horwitz, L. P.

AU - Strauss, Y.

PY - 1998/10

Y1 - 1998/10

N2 - We discuss some of the experimental motivation for the need for semigroup decay laws and the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips S-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these resonance (eigenfunctions of the generator f the semigroup) lie in the Lax-Phillips Hilbert space, and, therefore, all physical properties of the resonant states can be computed. We show that the parametrized relativistics quantum theory is an natural setting for the realization of the Lax-Phillips theory.

AB - We discuss some of the experimental motivation for the need for semigroup decay laws and the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips S-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these resonance (eigenfunctions of the generator f the semigroup) lie in the Lax-Phillips Hilbert space, and, therefore, all physical properties of the resonant states can be computed. We show that the parametrized relativistics quantum theory is an natural setting for the realization of the Lax-Phillips theory.

UR - http://www.scopus.com/inward/record.url?scp=0032277265&partnerID=8YFLogxK

U2 - 10.1023/A:1018894503871

DO - 10.1023/A:1018894503871

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AN - SCOPUS:0032277265

SN - 0015-9018

VL - 28

SP - 1607

EP - 1616

JO - Foundations of Physics

JF - Foundations of Physics

IS - 10

ER -