Transverse diffeomorphisms and spin-2 particles

Abstract

Recent experiments have detected, for the first time, gravitational waves predicted by Einstein's General Relativity, henceforth Einstein-Hilbert model (EH). According to such model, the carriers of the gravitational interaction (gravitons) are spin-2 particles without any mass. However, there always exist an experimental bound for a particle mass. The gravitational waves recent experiments have established an upper bound of 10^(-22)eV for the graviton's mass. Moreover, a massive graviton could help us to explain the accelerated expansion of the universe, discovered at the end of the 1990s. In this context, this project aims to study spin-2 particles with and without mass.In the usual scenario, the linearized EH model (LEH) is invariant under linearized diffeomorphisms (DIFF). Notwithstanding, it is known that the minimum required symmetry to get rid of spin-1 non-physical modes is the transverse diffeomorphisms (TDIFF). The TDIFF model, besides spin-2 particles, also describes spin-0 particles, both massless. The extensions of this symmetry are the DIFF (EH), a lot explored, and WTDIFF (Weyl + TDIFF) symmetries, recently investigated in some works. These three symmetries exhaust the possibilities to describe massless spin-2 particles in a consistent way using a symmetric rank-2 tensor.The EHL model can be modified by including a massive term which breaks the DIFF invariance giving rise to the traditional Fierz-Pauli model, which describes spin-2 massive particles and it is the basis of several new models of massive gravity investigated in the last decade as an attempt to overcome problems like the vDVZ mass discontinuity and the Boulware and Deser ghost.The target of this project is to investigate the TDIFF theory and its massive version in Minkowski (flat) space as well as in curved background spaces, providing the student with basic tools of quantum field theory and introducing him to particles propagation in curved background spaces.We also explore the fact that massless theories in D+1 dimensions can generate massive theories in D dimensions through a Kaluza-Klein dimensional reduction. This will be used in order to obtain a massive version of TDIFF from its higher dimensional massless counterpart. (AU)