Quantal time asymmetry: mathematical foundation and physical interpretation

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dc.creatorBohm, A.
dc.creatorBryant, P.
dc.creatorSato, Y.
dc.date2008-03-21
dc.date.accessioned2026-07-07T11:33:18Z
dc.date.available2026-07-07T11:33:18Z
dc.descriptionFor a quantum theory that includes exponentially decaying states and Breit-Wigner resonances, which are related to each other by the lifetime-width relation $τ=\frac{\hbar}Γ$, where $τ$ is the lifetime of the decaying state and $Γ$ the width of the resonance, one has to go beyond the Hilbert space and beyond the Schwartz-Rigged Hilbert Space $Φ\subset\mathcal{H}\subsetΦ^\times$ of the Dirac formalism. One has to distinguish between prepared states, using a space $Φ_-\subset\mat hcal{H}$, and detected observables, using a space $Φ_+\subset\mathcal{H}$, where $-(+)$ refers to analyticity of the energy wave function in the lower (upper) complex energy semiplane. This differentiation is also justified by causality: A state needs to be prepared first, before an observable can be measured in it. The axiom that will lead to the lifetime-width relation is that $Φ_+$ and $Φ_-$ are Hardy spaces of the upper and lower semiplane, respectively. Applying this axiom to the relativistic case for the variable $\s=p_μp^μ$ leads to semigroup transformations into the forward light cone (Einstein causality) and a precise definition of resonance mass and width.
dc.descriptionPlenary talk at the 5th International Symposium on Quantum Theory and Symmetries, July 22-28, 2007, Valladolid, Spain
dc.identifierhttps://arxiv.org/abs/0803.3233
dc.identifierhttp://arxiv.org/abs/0803.3233
dc.identifierJ.Phys.A41:304019,2008
dc.identifierdoi:10.1088/1751-8113/41/30/304019
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/197843
dc.subjectQuantum Physics
dc.titleQuantal time asymmetry: mathematical foundation and physical interpretation
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