Field and String Quantization in Curved Space-Times

Abstract

Perhaps the main challenge in theoretical physics today is unification of all interactions including gravity. At present, string theories appear as the best candidates to achieve such a unification. However, many technical and conceptual problems remain and a quantum theory of gravity is still not available. Continuous effort over the last quarter of a century has demonstrated the many difficulties encountered in repeated attempts to construct such a theory and has also indicated some of the particular properties that an eventual complete theory will have to possess. The amount of work in that direction can be by now presented in two different sets, which have mainly evolved (and remain) separated: (1) conceptual unification (introduction of the uncertainty principle in general relativity, the interpretation problem, quantum field theory (QFT) in curved space-time and by accelerated observers, Hawking radiation and its consequences, “wave function of the universe”,…); (2) grand unification (the unification of all interactions including gravity from the particle physics point of view. Gravity is considered as a massless spin-2 particle (the graviton, super-gravities, Kaluza-Klein theories, and the more successful superstrings). Whatever the final theory of the world will be, if it is to be a theory of everything, we would like to know what new understanding it will give us about the singularities of classical general relativity.