Introduction to the transversal difeomorfisms and Bardeen variables

• Grant number: 23/10876-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2023
• End date: September 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Denis Dalmazi
• Grantee: Bruno dos Santos Martins
• Host Institution: Faculdade de Engenharia (FEG). Universidade Estadual Paulista (UNESP). Campus de Guaratinguetá. Guaratinguetá , SP, Brazil

Abstract

It is known that the minimum symmetry needed to eliminate unwanted spin-1 degrees of freedom (ghosts) present in the symmetric tensor corresponds to transverse diffeomorphisms (TDiff). One can use the TDiff theory to describe massless particles of spin-2 and spin-0. The Tdiff theory depends upon a real arbitrary parameter that guarantees the unitarity of this theory for a certain range. This parameter allows us to obtain the Einstein-Hilbert or Weyl Transverse Diffeomorphism (WTDiff symmetry) Lagrangians, which correspond respectively to the linearization around the flat space of Einstein's general relativity and unimodular gravitation. The TDiff model also has non-linear versions where the determinant of the metric behaves like a scalar field. In this work we seek to introduce a minimal set of gauge invariants (not Lorentz covariants) called Bardeen's variables, already known for the Diff symmetry, now for the TDiff symmetry, in order to simplify the identification of the physical degrees of freedom, propagating and non-propagating ones. This minimal set of gauge invariants must have a higher spin version that will be investigated here for massless spin-3 particles (Fronsdal Lagrangian and its TDiff version).