Schroedinger's Cat is not Alone

We introduce the `Complete Wave Function' and deduce that all living beings, not just Schroedinger's cat, are actually described by a superposition of `alive' and `dead' quantum states; otherwise they would never die. Therefore this proposal provides a quantum mechanical explanation to the world-wide observation that we all pass away. Next we consider the Measurement problem in the framework of M-theory. For this purpose, together with Schroedinger's cat we also place inside the box Rasputin's cat, which is unaffected by poison. We analyse the system identifying its excitations (catons and catinos) and we discuss its evolution: either to a classical fight or to a quantum entanglement. We also propose the $BSV\Psi$ scenario, which implements the Complete Wave Function as well as the Big Bang and the String Landscape in a very (super)natural way. Then we test the gravitational decoherence of the entangled system applying an experimental setting due to Galileo. We also discuss the Information Loss paradox. For this purpose we consider a massless black cat falling inside a massive black hole. After that we outline a method to compute the contribution of black cats to the dark matter of the universe. Finally, in the spirit of Schroedinger, we propose that next generation double-slit experiments should use cats as projectiles. Cat interferometry will inevitably lead to the `Many Cats' interpretation of Quantum Mechanics, allowing to shed new light on old mysteries and paradoxes. For example, according to this interpretation, conservative estimates show that decision making of a single domestic cat will create about 550 billion whole universes every day, with as many replicas of itself.Comment: Prepared for April Fools' Day. Latex, 12 page

Recent Results on N=2 Superconformal Algebras

In the last six years remarkable developments have taken place concerning the representation theory of N=2 superconformal algebras. Here we present the highlights of such developments.Comment: Latex, 11 pages. Invited talk presented at the International Conference on Conformal Field Theory and Integrable Models, Landau Institute, Moscow (Russia), June 1999, and at the 6th International Wigner Symposium, Bogazici University, Istambul (Turkey), August 199

The Fermi Paradox in the light of the Inflationary and Brane World Cosmologies

The Fermi Paradox is discussed in the light of the inflationary and brane world cosmologies. We conclude that some brane world cosmologies may be of relevance for the problem of civilizations spreading across our galaxy, strengthening the Fermi Paradox, but not the inflationary cosmologies, as has been proposed.Comment: Chapter of the book `Trends in General Relativity and Quantum Cosmology', Nova Science Eds, New York, 2006, with several minor improvement

The Adapted Ordering Method for the Representation Theory of Lie Algebras and Superalgebras and their Generalizations

In 1998 the Adapted Ordering Method was developed for the study of the representation theory of the superconformal algebras in two dimensions. It allows: to determine the maximal dimension for a given type of space of singular vectors, to identify all singular vectors by only a few coefficients, to spot subsingular vectors and to set the basis for constructing embedding diagrams. In this talk I introduce the present version of the Adapted Ordering Method, published in J. Phys. A: Math. Theor. 41 (2008) 045201, which can be applied to general Lie algebras and superalgebras and their generalizations, provided they can be triangulated.Comment: Invited talk at The 17th Colloquium "Integrable Systems and Quantum Symmetries", Prague, June 19-21, 2008. Very pedagogical. Six page

No isomorphism between the affine s^l(2)\hat sl(2) algebra and the N=2 superconformal algebras

Since 1999 it became obvious that the would be `isomorphism' between the affine $\hat sl(2)$ algebra and the N=2 superconformal algebras, proposed by some authors, simply does not work. However, this issue was never properly discussed in the literature and, as a result, some confusion still remains. In this article we finally settle down, clearly and unambiguously, the true facts: there is no isomorphism between the affine $\hat sl(2)$ algebra and the N=2 superconformal algebras.Comment: 16 pages, 4 figure

Remarks on Global Anomalies in DHS Orientifolds

I review the main features of the Dijkstra-Huiszoon-Schellekens (DHS) orientifolds and report on the search for global anomalies that Schellekens and the author have performed for these models.Comment: Invited talk given at the Strings 2006 Workshop, Shanghai (China), June 2006, 6 page

Brane Worlds, the Subanthropic Principle and the Undetectability Conjecture

In the recent article `Conflict between anthropic reasoning and observation'(gr-qc/0303070) Ken D. Olum, using some inflation-based ideas and the anthropic premise that we should be typical among all intelligent observers in the Universe, arrives at the puzzling conclusion that `we should find ourselves in a large civilization (of galactic size) where most observers should be, while in fact we do not'. In this note we discuss the intriguing possibility whether we could be in fact immersed in a large civilization without being aware of it. Our conclusion is that this possibility cannot be ruled out provided two conditions are met, that we call the Subanthropic Principle and the Undetectability Conjecture. ----- En el reciente articulo `Conflicto entre razonamiento antropico y observacion' Ken D. Olum, basandose en algunas ideas sobre la inflacion cosmologica y en la premisa antropica de que tenemos que ser tipicos entre los observadores inteligentes del Universo, llega a la sorprendente conclusion de que `deberiamos encontrarnos en una civilizacion grande (de tamanio galactico) al igual que la mayoria de los observadores, mientras que de hecho no lo estamos'. En este articulo discutimos la posibilidad de que nuestra civilizacion este de hecho inmersa en una civilizacion grande, sin que seamos conscientes de ello. Nuestra conclusion es que esta posibilidad no puede descartarse si se cumplen dos condiciones, que llamamos el Principio Subantropico y la Conjetura de Indetectabilidad.Comment: Dedicated to Giordano Bruno, Latex, 15 pages. Four new footnotes, one last paragraph in the Appendix and several minor improvements in the redaction. Spanish version also availabl

Construction Formulae for Singular Vectors of the Topological and of the Ramond N=2 Superconformal Algebras

We write down one-to-one mappings between the singular vectors of the Neveu-Schwarz N=2 superconformal algebra and $16 + 16$ types of singular vectors of the Topological and of the Ramond N=2 superconformal algebras. As a result one obtains construction formulae for the latter using the construction formulae for the Neveu-Schwarz singular vectors due to D\"orrzapf. The indecomposable singular vectors of the Topological and of the Ramond N=2 algebras (`no-label' and `no-helicity' singular vectors) cannot be mapped to singular vectors of the Neveu-Schwarz N=2 algebra, but to {\it subsingular} vectors, for which no construction formulae exist.Comment: 27 pages, LaTe

The Adapted Ordering Method in Representation Theory

In 1998 the Adapted Ordering Method was developed for the representation theory of the superconformal algebras. This method, which proves to be very powerful, can be applied to most algebras and superalgebras, however. It allows: to determine maximal dimensions for a given type of singular vector space, to identify all singular vectors by only a few coefficients, to spot subsingular vectors and to set the basis for constructing embedding diagrams. In this article we present the Adapted Ordering Method for general algebras and superalgebras which admit a triangulation and review briefly the results obtained for the Virasoro algebra and for the N=2 and Ramond N=1 superconformal algebras.Comment: Several improvements in the redaction. Conclusions and references added. Latex, 11 page

Construction Formulae for Singular Vectors of the Topological N=2 Superconformal Algebra

The Topological N=2 Superconformal algebra has 29 different types of singular vectors (in complete Verma modules) distinguished by the relative U(1) charge and the BRST-invariance properties of the vector and of the primary on which it is built. Whereas one of these types only exists at level zero, the remaining 28 types exist for general levels and can be constructed already at level 1. In this paper we write down one-to-one mappings between 16 of these types of topological singular vectors and the singular vectors of the Antiperiodic NS algebra. As a result one obtains construction formulae for these 16 types of topological singular vectors using the construction formulae for the NS singular vectors due to Doerrzapf.Comment: Latex, 13 page