VI Mexican School on Gravitation and Mathematical Physics

Abstract

The Mexican School on Gravitation and Mathematical Physics,sponsored by the Mexican Physical Society, started in the early 1990s.The aim of the school is to consider different topics at the frontiersof current research on gravitation, field theory and mathematicalphysics. It is held every two years and a different theme is chosen oneach occasion. The school, which is oriented towards advanced graduatestudents and non-expert researchers, has been gaining reputationbecause of the quality of the lectures given by leaders in eachfield. On previous occasions, the subjects covered have been Supergravity and Mathematical Physics, Branes, Black Holes, Early Universe and Observational Cosmology, and thespeakers have included A. Ashtekar, A. Balachandran, J. Barrow,B. Carter, P. Chrusciel, G. Gibbons, M. Heusler, W. Israel,F. Müller-Hoisen, R. Kallosh, A. Linde, Y. Neeman, R. Myers,A. Peet, L. Randall, C. Rovelli, L. Smolin, R. Sorkin, P. VanNiewenhuizen, R. Wald, among other top ranked physicists.Let us now turn our attention to the current edition of theschool. The two great pillars of twentieth century physics are quantummechanics and the general theory of relativity (GR) and, in spite oftheir great independent successes, it has been enormously difficult tocombine them into a single theoretical framework. It seems that thenonlinearities of GR and its attractive nature pose severe problemsto understand its possible quantum nature, e.g. renormalizationissues. In order to solve this and other quantization problems, aswell as to try to unify gravity with the other quantum fields(electromagnetic, weak, and strong fields), in the past decadesseveral different approaches to quantum gravity have been developed.In view of the fundamental importance of such topics today, the theme Approaches to Quantum Gravity was chosen for the VI MexicanSchool on Gravitation and Mathematical Physics. We considered thatsubjects like loop quantum gravity (quantum geometry), spinfoams, De Sitter vacua in string theory and string landscape, black holes in string theory, time–spacenon-commutativity, and some related topics on classicalgravity would give a good picture about the current status of modernquantum gravity theories. Even though these approaches share the samegoal, the basis on which they rely and the ways in which theytackle the quantization of gravity are conceptually and technicallyvery different. As a result there is a richness of viewpoints on thesubject. The aim of the VI Mexican School on Gravitation andMathematical Physics was therefore to present these differentviewpoints on quantum gravity, including the most recent theoreticalresults and the way in which these approaches attempt to get closer toexperimental predictions. In addition, during the school wediscussed open fundamental issues such as problems in classical andquantum physics related to the quantization of gravity, and theunification of the fundamental interactions of nature, among others.As in previous schools, the topics were covered by leaders in thefield, and the general perception by the participants was that thisgoal was certainly accomplished (not to mention the beautiful settingfor the school in the Mexican Caribbean at Playa del Carmen). Aboutone hundred people participated from all over the world and we areindebted to all of them. Undoubtedly, the school would have not beenpossible without the main courses and plenary lectures. Therefore, ourdeep gratitude goes to all the invited speakers. The school wascomplemented with more specialized topics presented in parallelsessions, some of which are included in these proceedings.Finally, the goal of the school would certainly be incomplete if therewere not some record of the ideas presented during the week inNovember 2004. We therefore warmly thank all the contributors who madepossible the publication of the present proceedings.