dorsal/arxiv
View SchemaComplex Energies and Beginnings of Time Suggest a Theory of Scattering and Decay
| Authors | A. Bohm, P. Kielanowski, S. Wickramasekara |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510060 |
| URL | https://arxiv.org/abs/quant-ph/0510060 |
| DOI | 10.1016/j.aop.2006.02.016 |
Abstract
Many useful concepts for a quantum theory of scattering and decay (like Lippmann-Schwinger kets, purely outgoing boundary conditions, exponentially decaying Gamow vectors, causality) are not well defined in the mathematical frame set by the conventional (Hilbert space) axioms of quantum mechanics. Using the Lippmann-Schwinger equations as the takeoff point and aiming for a theory that unites resonances and decay, we conjecture a new axiom for quantum mechanics that distinguishes mathematically between prepared states and detected observables. Suggested by the two signs $\pm i\epsilon$ of the Lippmann-Schwinger equations, this axiom replaces the one Hilbert space of conventional quantum mechanics by two Hardy spaces. The new Hardy space theory automatically provides Gamow kets with exponential time evolution derived from the complex poles of the $S$-matrix. It solves the causality problem since it results in a semigroup evolution. But this semigroup brings into quantum physics a new concept of the semigroup time $t=0$, a beginning of time. Its interpretation and observations are discussed in the last section.
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"abstract": "Many useful concepts for a quantum theory of scattering and decay (like\nLippmann-Schwinger kets, purely outgoing boundary conditions, exponentially\ndecaying Gamow vectors, causality) are not well defined in the mathematical\nframe set by the conventional (Hilbert space) axioms of quantum mechanics.\nUsing the Lippmann-Schwinger equations as the takeoff point and aiming for a\ntheory that unites resonances and decay, we conjecture a new axiom for quantum\nmechanics that distinguishes mathematically between prepared states and\ndetected observables. Suggested by the two signs $\\pm i\\epsilon$ of the\nLippmann-Schwinger equations, this axiom replaces the one Hilbert space of\nconventional quantum mechanics by two Hardy spaces. The new Hardy space theory\nautomatically provides Gamow kets with exponential time evolution derived from\nthe complex poles of the $S$-matrix. It solves the causality problem since it\nresults in a semigroup evolution. But this semigroup brings into quantum\nphysics a new concept of the semigroup time $t=0$, a beginning of time. Its\ninterpretation and observations are discussed in the last section.",
"arxiv_id": "quant-ph/0510060",
"authors": [
"A. Bohm",
"P. Kielanowski",
"S. Wickramasekara"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.aop.2006.02.016",
"title": "Complex Energies and Beginnings of Time Suggest a Theory of Scattering and Decay",
"url": "https://arxiv.org/abs/quant-ph/0510060"
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