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

Indigenous Movements, Democracy, and U.S. Interests in Latin America

Indigenous movements have become increasingly powerful in the last couple of decades and they are now important political actors in some South American countries, such as Bolivia, Ecuador, and, to a lesser extent, Peru and Chile. The rise of indigenous movements has provoked concern among U.S. policymakers and other observers who have feared that these movements will exacerbate ethnic polarization, undermine democracy, and jeopardize U.S. interests in the region. This paper argues that concern over the rise of indigenous movements is greatly exaggerated. It maintains that the rise of indigenous movements has not brought about a market increase in ethnic polarization in the region because most indigenous organizations have been ethnically inclusive and have eschewed violence. Although the indigenous movements have at times demonstrated a lack of regard for democratic institutions and procedures, they have also helped deepen democracy in the Andean region by promoting greater political inclusion and participation and by aggressively combating ethnic discrimination and inequality. Finally, this study suggests that the indigenous population has opposed some U.S. –sponsored initiatives, such as coca eradication and market reform, for legitimate reasons. Such policies have had some negative environmental, cultural, and economic consequences for indigenous people, which U.S. policymakers should try to address. The conclusion provides some specific policy recommendations on how to go about this

Singing Blackness across Borders. Capeyuye and Mascogo Identity in Northern Mexico [abstract only]

This paper takes capeyuye [spiritual singing] as a point of departure to study the Mascogos’ continuous struggle to define themselves as binational people, as Afro- Seminoles living in Coahuila, Mexico. By reflecting on the intersections of race, nationality, and the body within the specificities of Mascogo border culture and history, the paper problematizes Anne Anlin Cheng’s notion of “racial melancholia,” suggesting that self rejection might be a more strategic move than she acknowledges to be. In the end, the author coins the term “dialectical soundings” and propose that the singing of spirituals among the Mascogos in fact renders Blackness visible in the context of the Mexican border essentialist racial discourses

A Pedestrian Introduction to Gamow Vectors

The Gamow vector description of resonances is compared with the S-matrix and the Green function descriptions using the example of the square barrier potential. By imposing different boundary conditions on the time independent Schrodinger equation, we obtain either eigenvectors corresponding to real eigenvalues and the physical spectrum or eigenvectors corresponding to complex eigenvalues (Gamow vectors) and the resonance spectrum. We show that the poles of the S matrix are the same as the poles of the Green function and are the complex eigenvalues of the Schrodinger equation subject to a purely outgoing boundary condition. The intrinsic time asymmetry of the purely outgoing boundary condition is discussed. Finally, we show that the probability of detecting the decay within a shell around the origin of the decaying state follows an exponential law if the Gamow vector (resonance) contribution to this probability is the only contribution that is taken into account.Comment: 25 RevTex pages, 3 figure

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 role of the rigged Hilbert space in Quantum Mechanics

There is compelling evidence that, when continuous spectrum is present, the natural mathematical setting for Quantum Mechanics is the rigged Hilbert space rather than just the Hilbert space. In particular, Dirac's bra-ket formalism is fully implemented by the rigged Hilbert space rather than just by the Hilbert space. In this paper, we provide a pedestrian introduction to the role the rigged Hilbert space plays in Quantum Mechanics, by way of a simple, exactly solvable example. The procedure will be constructive and based on a recent publication. We also provide a thorough discussion on the physical significance of the rigged Hilbert space.Comment: 29 pages, 2 figures; a pedestrian introduction to the rigged Hilbert spac

Taming Rebellion in South America, 1830-1929

South America was plagued by internal conflict during the 19th century that destabilized the region’s economies and political systems. At the beginning of the 20th century, however, levels of political violence throughout the region declined dramatically. Existing scholarship has paid surprisingly little attention to this historic transformation in part because of the absence of comprehensive data on revolts. Drawing on the work of historians, we create a comprehensive dataset on revolts in ten South American countries from 1830 to 1929, and we develop an original typology of revolts based on the origins of the rebel leaders. We find that revolts from outside the state apparatus declined dramatically during this period, while revolts from inside the state, such as coups, did not. We hypothesize that increases in the size and professionalization of the military, which were driven by the export boom and the threat of international conflict, are fundamental to explain these regional patterns. We test the observational implications of our theory through historical narratives and a series of regression analyses on cross-national time-series data