Reply to ``Comment on `On the inconsistency of the Bohm-Gadella theory with quantum mechanics'''

In this reply, we show that when we apply standard distribution theory to the Lippmann-Schwinger equation, the resulting spaces of test functions would comply with the Hardy axiom only if classic results of Paley and Wiener, of Gelfand and Shilov, and of the theory of ultradistributions were wrong. As well, we point out several differences between the ``standard method'' of constructing rigged Hilbert spaces in quantum mechanics and the method used in Time Asymmetric Quantum Theory.Comment: 13 page

The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part I

We exemplify the way the rigged Hilbert space deals with the Lippmann-Schwinger equation by way of the spherical shell potential. We explicitly construct the Lippmann-Schwinger bras and kets along with their energy representation, their time evolution and the rigged Hilbert spaces to which they belong. It will be concluded that the natural setting for the solutions of the Lippmann-Schwinger equation--and therefore for scattering theory--is the rigged Hilbert space rather than just the Hilbert space.Comment: 34 pages, 1 figur

Primers resultats de l'estudi de la ceràmica terra sigillata de Baetulo: circulació ceràmica i aportacions cronològiques a la ciutat

Les actuacions arqueologiques portades a terme des dels anys se tanta a la ciutat de Badalona, han permes posar al descobert una part important d'estructures corresponents a la ciutat romana de Baetulo. A partir d'aquestes excavacions, l' analisi específica de la ceramica terra sigillata documentada en determinats contextos estratigrafics, on aquest tipus ceramic és l'element basic de datació, ens ha permes realitzar una revisió de les cronologies proposades inicialment per a aquests estrats i per a les estructures associades. Aquesta revisió, que afecta el període que va del regnat d' August fms a epoca flavia, ha suposat la clarificació del material de terra sigillata recuperat i, en alguns casos, la modificació de la interpretació de la seqüencia estratigrafica i la se va datació

F-transforms for the definition of contextual fuzzy partitions

Fuzzy partitions can be defined in many different ways, but usually, it is done taking into account the whole universe. In this paper, we present a method to define fuzzy partitions according to those elements in the universe holding certain fuzzy attribute. Specifically, we show how to define those fuzzy partitions by means of F-transforms.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech This work has been partially supported by the Spanish Ministry of Science by the projects TIN15-70266-C2-P-1 and TIN2016-76653-

The non-equilibrium work relation. Thermodynamic analysis and microscopic foundations

We discuss the conditions for which the non-equilibrium work relation is valid by means of thermodynamic and microscopic arguments.Comment: 16 pages 1 figur

The Importance of Boundary Conditions in Quantum Mechanics

We discuss the role of boundary conditions in determining the physical content of the solutions of the Schrodinger equation. We study the standing-wave, the ``in,'' the ``out,'' and the purely outgoing boundary conditions. As well, we rephrase Feynman's $+i \epsilon$ prescription as a time-asymmetric, causal boundary condition, and discuss the connection of Feynman's $+i \epsilon$ prescription with the arrow of time of Quantum Electrodynamics. A parallel of this arrow of time with that of Classical Electrodynamics is made. We conclude that in general, the time evolution of a closed quantum system has indeed an arrow of time built into the propagators.Comment: Contribution to the proceedings of the ICTP conference "Irreversible Quantum Dynamics," Trieste, Italy, July 200

The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part II: The analytic continuation of the Lippmann-Schwinger bras and kets

The analytic continuation of the Lippmann-Schwinger bras and kets is obtained and characterized. It is shown that the natural mathematical setting for the analytic continuation of the solutions of the Lippmann-Schwinger equation is the rigged Hilbert space rather than just the Hilbert space. It is also argued that this analytic continuation entails the imposition of a time asymmetric boundary condition upon the group time evolution, resulting into a semigroup time evolution. Physically, the semigroup time evolution is simply a (retarded or advanced) propagator.Comment: 32 pages, 3 figure