Quantum Field Theory In Curved Spacetimes

Abstract

QFT in curved spacetime is a semi classical approximation to any theory of quantum gravity which as of date remains elusive to nd. Though the foundations of this subject were rmly established as early as 1970, there is still a lot of debate and discussion which has sometimes culminated in 'wars' on topics such as information paradox, the violation of basic symmetries in black holes, the nal stages of evaporation of a black hole and many others even as of today. We work in a paradigm where gravity is considered as a classical theory and the matter elds are quantum in nature. Also we work at energy scales much less than the Plank scale so that we are justi ed in neglecting the non perturbative e ects of the quantum nature of gravity. As we shall see non trivial e ects of gravitation occur in the quantum eld modes only then the wavelength of the modes is of the order of characteristic length scales of the background metric which implies we can verify the predicted results only at large energies which were prevalent at early times just after the big bang. As a consequence most of the results remain theoretical and experimental checks are rare. Hawking's result of thermal radiation from black holes and the connection between quantum black holes and thermodynamics has shed some light for new fundamental physics in which gravity, thermodynamics and QFT pull all the strings. This could in turn lead to looking at physics with new eyes and making advances that have some experimental checks. It is with this motivation that we embark on a journey of understanding these historical and path breaking results. The motivation to study curved space QFT is multidimensional as a case about it being a rst approximation to quantum gravity has been made. The study of black holes and e ects like Hawking radiation are consistency checks for many new theories like DBI theory, AdS/CFT duality thus anyone interested exploring these elds must have a rm knowledge of curved space QFT. Also the study of anomalies is central to the understanding of low energy limit of string theories as well as statistical physics. This subject consolidates previous knowledge and brings one to the doorstep of new and exciting physics which is reason enough to pursue it.