arXiv subjects

R. R. Lino dos Santos

Publications and source records attributed to R. R. Lino dos Santos.

3 recordsLinked to original sources

arXiv2024

Generators of the Poincaré Group for arbitrary tensors and spinor-tensors

In this work, we systematically derive explicit expressions for the Poincaré Group generators on arbitrary-rank tensors and spinor-tensors in $D=3+1$ and $D=2+1$ spacetimes, thus generalizing previous works in the literature for the groups $ISO(3,1)$ and $ISO(2,1)$. From the Casimir eigenvalue equations, we demonstrate in a model-independent way the Fierz-Pauli constraints for massive particles for spins $\mathfrak{s}=5/2$, 3, and 4 in $D=3+1$ and helicities $α=5/2$, 3, and 4 in $D=2+1$ dimensions. We also comment on the demonstration of the Fierz-Pauli constraints for the general case of arbitrary spin (helicity).

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arXiv2021

The dimensional reduction of linearized spin-2 theories invariant under transverse diffeomorphisms

Here we perform the Kaluza-Klein dimensional reduction from $D+1$ to $D$ dimensions of massless Lagrangians described by a symmetric rank-2 tensor and invariant under transverse differmorphisms (TDiff). They include the linearized Einstein-Hilbert theory, linearized unimodular gravity and scalar tensor models. We obtain simple expressions in terms of gauge invariant field combinations and show that unitarity is preserved in all cases. After fixing a gauge, the reduced model becomes a massive scalar tensor theory. We show that the diffeomorphism (Diff) symmetry, instead of TDiff, is a general feature of the massless sector of consistent massive scalar tensor models. We discuss some subtleties when eliminating Stückelberg fields directly at action level as gauge conditions. We also show that the reduced models all have a smooth massless limit. A non local connection between the massless sector of the scalar tensor theory and the pure tensor TDiff model leads to a parametrization of the non conserved source which naturally separates spin-0 and spin-2 contributions in the pure tensor theory. The case of curved backgrounds is also investigated. If we truncate the non minimal couplings to linear terms in the curvature, vector and scalar constraints require Einstein spaces as in the Diff and WTDiff (Weyl plus Diff) cases. We prove that our linearized massive scalar tensor models admit those curved background extensions.

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arXiv2018

Higher order self-dual models for spin-3 particles in $D=2+1$

In $D=2+1$ dimensions, elementary particles of a given helicity can be described by local Lagrangians (parity singlets). By means of a "soldering" procedure two opposite helicities can be joined together and give rise to massive spin-$s$ particles carrying both helicities $\pm s$ (parity doublets), such Lagrangians can also be used in $D=3+1$ to describe massive spin-$s$ particles. From this point of view the parity singlets (self-dual models) in $D=2+1$ are the building blocks of real massive elementary particles in $D=3+1$. In the three cases $s=1,\, 3/2,\, 2$ there are $2s$ self-dual models of order $1,2, \cdots, 2s$ in derivatives. In the spin-3 case the 5th order model is missing in the literature. Here we deduce a 5th order spin-3 self-dual model and fill up this gap. It is shown to be ghost free by means of a master action which relates it with the top model of 6th order. We believe that our approach can be generalized to arbitrary integer spin-$s$ in order to obtain the models of order $2s$ and $2s-1$. We also comment on the difficulties in relating the 5th order model with their lower order duals.

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