Classical and quantum theory of the massive spin-two field

Abstract

In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz-Pauli constraints via three different methods: the eigenvalue equations for the Casimir invariants of the Poincaré group, a Lagrangian approach, and a covariant Hamilton formalism. We also present the conserved quantities, the solution of the equations of motion in terms of polarization tensors, and the tree-level propagator. We then discuss canonical quantization by postulating commutation relations for creation and annihilation operators. We express the energy, momentum, and spin operators in terms of the former. As an application, quark-antiquark currents for tensor mesons are presented. In particular, the current for tensor mesons with quantum numbers $J^{PC}=2^{-+}$ is, to our knowledge, given here for the first time.

43 pages

References in corpus (4)

• Infrared-modified gravities and massive gravitons
• The mass spectrum and strong decays of isoscalar tensor mesons
• Masses and decay constants of the heavy tensor mesons with QCD sum rules
• A note on the nonuniqueness of the massive Fierz-Pauli theory and spectator fields

Cited by in corpus (11)

• Black hole radiation of massive spin-2 particles in (3+1) dimensions
• Phenomenology of pseudotensor mesons and the pseudotensor glueball
• Phenomenology of $J^{PC}=3^{--}$ tensor mesons
• Production of the $X(4014)$ as the spin-2 partner of $X(3872)$ in $e^{+}{e}^{-}$ collisions
• Anomalous interactions between mesons with nonzero spin and glueballs
• Ordinary and exotic mesons in the extended Linear Sigma Model
• From well-known tensor mesons to yet unknown axial-tensor mesons
• Constraints imposed by the partial wave amplitudes on the decays of $J=1,2$ mesons
• Massive spin-2 particles in a curved background via a nonsymmetric tensor
• Conventional mesons below 2 GeV
• Translation gauge field theory of gravity in Minkowski spacetime