Euclidean self-dual gravity: Ashtekar variables without gauge fixing
arXiv:2312.12947 · doi:10.1103/PhysRevD.109.064047
Abstract
The Gotay-Nester-Hinds method is used in this paper to study the Hamiltonian formulation of the Euclidean self-dual action. This action can be used to arrive at the complex Ashtekar formulation of General Relativity or a real connection formulation for Euclidean General Relativity. The main result of the paper is a derivation of the Ashtekar formulation for Euclidean gravity without using any gauge fixing. It is interesting to compare this derivation with the one corresponding to the Holst action. In particular it is worth noting that no "tertiary" constraints appear in the case considered in the present paper.
29 pages, no figures
References in corpus (15)
- Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
- Reality Conditions and Ashtekar Variables: a Different Perspective
- Towards an Anomaly-Free Quantum Dynamics for a Weak Coupling Limit of Euclidean Gravity
- New boundary variables for classical and quantum gravity on a null surface
- 4d Lorentzian Holst action with topological terms
- The G_Newton --> 0 Limit of Euclidean Quantum Gravity
- The constraint algebra in Smolins' limit of 4d Euclidean Gravity
- Dirac's algorithm in the presence of boundaries: a practical guide to a geometric approach
- Manifestly Lorentz-covariant variables for the phase space of general relativity
- Canonical analysis of Holst action without second-class constraints
- Concise symplectic formulation for tetrad gravity
- Hamiltonian Gotay-Nester-Hinds analysis of the parametrized unimodular extension of the Holst action
- Covariant Origin of the model for Euclidean Quantum Gravity
- Barbero-like variables derived from Holst action
- Revisiting the solution of the second-class constraints of the Holst action