Fermions coupled to the Palatini action in $n$ dimensions

Abstract

We study minimal and nonminimal couplings of fermions to the Palatini action in $n$ dimensions ($n\ge 3$) from the Lagrangian and Hamiltonian viewpoints. The Lagrangian action considered is not, in general, equivalent to the Einstein-Dirac action principle. However, by choosing properly the coupling parameters, it is possible to give a first-order action fully equivalent to the Einstein-Dirac theory in a spacetime of dimension four. By using a suitable parametrization of the vielbein and the connection, the Hamiltonian analysis of the general Lagrangian is given, which involves manifestly Lorentz-covariant phase-space variables, a real noncanonical symplectic structure, and only first-class constraints. Additional Hamiltonian formulations are obtained via symplectomorphisms, one of them involving half-densitized fermions. To confront our results with previous approaches, the time gauge is imposed.

It matches published version. We have improved a line breaking

References in corpus (3)

• Canonical Gravity with Fermions
• Canonical analysis of $n$-dimensional Palatini action without second-class constraints
• Hamiltonian analysis of fermions coupled to the Holst action