dorsal/arxiv
View SchemaOn the inconsistency of the Bohm-Gadella theory with quantum mechanics
| Authors | R. de la Madrid |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0606186 |
| URL | https://arxiv.org/abs/quant-ph/0606186 |
| DOI | 10.1088/0305-4470/39/29/017 |
| Journal | J.Phys. A: Math. Gen. 39 (2006) 9255-9268 |
Abstract
The Bohm-Gadella theory, sometimes referred to as the Time Asymmetric Quantum Theory of Scattering and Decay, is based on the Hardy axiom. The Hardy axiom asserts that the solutions of the Lippmann-Schwinger equation are functionals over spaces of Hardy functions. The preparation-registration arrow of time provides the physical justification for the Hardy axiom. In this paper, it is shown that the Hardy axiom is incorrect, because the solutions of the Lippmann-Schwinger equation do not act on spaces of Hardy functions. It is also shown that the derivation of the preparation-registration arrow of time is flawed. Thus, Hardy functions neither appear when we solve the Lippmann-Schwinger equation nor they should appear. It is also shown that the Bohm-Gadella theory does not rest on the same physical principles as quantum mechanics, and that it does not solve any problem that quantum mechanics cannot solve. The Bohm-Gadella theory must therefore be abandoned.
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"abstract": "The Bohm-Gadella theory, sometimes referred to as the Time Asymmetric Quantum\nTheory of Scattering and Decay, is based on the Hardy axiom. The Hardy axiom\nasserts that the solutions of the Lippmann-Schwinger equation are functionals\nover spaces of Hardy functions. The preparation-registration arrow of time\nprovides the physical justification for the Hardy axiom. In this paper, it is\nshown that the Hardy axiom is incorrect, because the solutions of the\nLippmann-Schwinger equation do not act on spaces of Hardy functions. It is also\nshown that the derivation of the preparation-registration arrow of time is\nflawed. Thus, Hardy functions neither appear when we solve the\nLippmann-Schwinger equation nor they should appear. It is also shown that the\nBohm-Gadella theory does not rest on the same physical principles as quantum\nmechanics, and that it does not solve any problem that quantum mechanics cannot\nsolve. The Bohm-Gadella theory must therefore be abandoned.",
"arxiv_id": "quant-ph/0606186",
"authors": [
"R. de la Madrid"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1088/0305-4470/39/29/017",
"journal_ref": "J.Phys. A: Math. Gen. 39 (2006) 9255-9268",
"title": "On the inconsistency of the Bohm-Gadella theory with quantum mechanics",
"url": "https://arxiv.org/abs/quant-ph/0606186"
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