Hamiltonian analysis of Poincar\'e gauge theory scalar modes

TL;DR

This paper uses Hamiltonian formalism to analyze the dynamics of scalar modes in Poincaré gauge gravity, identifying conditions for their propagation and gauge nature, and classifying constraints.

Contribution

It provides the first explicit Hamiltonian analysis of non-trivial scalar modes in Poincaré gauge theory, including their constraints and gauge properties.

Findings

Massive spin-0^- mode propagates normally.

Massless spin-0^- mode is pure gauge.

Both scalar modes can be viable under certain conditions.

Abstract

The Hamiltonian constraint formalism is used to obtain the first explicit complete analysis of non-trivial viable dynamic modes for the Poincar\'e gauge theory of gravity. Two modes with propagating spin-zero torsion are analyzed. The explicit form of the Hamiltonian is presented. All constraints are obtained and classified. The Lagrange multipliers are derived. It is shown that a massive spin-$0^-$ mode has normal dynamical propagation but the associated massless $0^-$ is pure gauge. The spin-$0^+$ mode investigated here is also viable in general. Both modes exhibit a simple type of ``constraint bifurcation'' for certain special field/parameter values.