Classical and quantum theory of the massive spin-two field

TL;DR

This paper reviews the classical and quantum field theory of massive spin-two fields, deriving equations of motion, constraints, and propagators, and introduces a novel tensor meson current for the first time.

Contribution

It provides a comprehensive derivation of the equations of motion, constraints, and propagators for massive spin-two fields using multiple methods, including a new tensor meson current.

Findings

Derived equations of motion and constraints via three methods

Presented the first tensor meson current for $J^{PC}=2^{-+}$

Expressed energy, momentum, and spin operators in terms of creation and annihilation operators

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 Poincar\'{e} 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.