Hamiltonian Analysis of Poincar\'e Gauge Theory: Higher Spin Modes

TL;DR

This paper uses Hamiltonian analysis to investigate higher spin modes in Poincaré gauge theory of gravity, revealing issues like constraint bifurcation that challenge the theory's viability.

Contribution

It provides a Hamiltonian framework to test nonlinear constraints in PGT, identifying problematic modes and evaluating the linearized theory of Kuhfuss and Nitsch.

Findings

Higher spin modes exhibit constraint bifurcation.

Pure spin 1 and 2 modes fail the nonlinear constraint test.

Linearized KRNJ86 theory does not pass the nonlinear constraint analysis.

Abstract

We examine several higher spin modes of the Poincar\'e gauge theory (PGT) of gravity using the Hamiltonian analysis. The appearance of certain undesirable effects due to non-linear constraints in the Hamiltonian analysis are used as a test. We find that the phenomena of field activation and constraint bifurcation both exist in the pure spin 1 and the pure spin 2 modes. The coupled spin-$0^-$ and spin-$2^-$ modes also fail our test due to the appearance of constraint bifurcation. The ``promising'' case in the linearized theory of PGT given by Kuhfuss and Nitsch (KRNJ86) likewise does not pass. From this analysis of these specific PGT modes we conclude that an examination of such nonlinear constraint effects shows great promise as a strong test for this and other alternate theories of gravity.