Dirac and Lagrangian reductions in the canonical approach to the first order form of the Einstein-Hilbert action
arXiv:hep-th/0507074 · doi:10.1016/j.aop.2005.09.009
Abstract
It is shown that the Lagrangian reduction, in which solutions of equations of motion that do not involve time derivatives are used to eliminate variables, leads to results quite different from the standard Dirac treatment of the first order form of the Einstein-Hilbert action when the equations of motion correspond to the first class constraints. A form of the first order formulation of the Einstein-Hilbert action which is more suitable for the Dirac approach to constrained systems is presented. The Dirac and reduced approaches are compared and contrasted. This general discussion is illustrated by a simple model in which all constraints and the gauge transformations which correspond to first class constraints are completely worked out using both methods in order to demonstrate explicitly their differences. These results show an inconsistency in the previous treatment of the first order Einstein-Hilbert action which is likely responsible for problems with its canonical quantization.
arXiv comment40 pages
References in corpus (11)
- Real Ashtekar Variables for Lorentzian Signature Space-times
- Dilaton Gravity in Two Dimensions
- Lectures on Loop Quantum Gravity
- The physical gravitational degrees of freedom
- Nonsymmetric Gravity Theories: Inconsistencies and a Cure
- The internal description of a causal set: What the universe looks like from the inside
- Dirac versus reduced phase space quantization for systems admitting no gauge conditions
- A Canonical Approach to the Einstein-Hilbert Action in Two Spacetime Dimensions
- Peculiarities of the Canonical Analysis of the First Order Form of the Einstein-Hilbert Action in Two Dimensions in Terms of the Metric Tensor or the Metric Density
- Gravitational Constraint Combinations Generate a Lie Algebra
- Linear derivative Cartan formulation of General Relativity
Cited by in corpus (14)
- Hypersurface foliation approach to renormalization of ADM formulation of gravity
- Hamiltonian formulation of tetrad gravity: three dimensional case
- The Canonical Structure of the First Order Einstein-Hilbert Action
- On Hamiltonian formulation of the Einstein-Hilbert action in two dimensions
- The Hamiltonian of Einstein affine-metric formulation of General Relativity
- Two-dimensional metric and tetrad gravities as constrained second order systems
- Translational invariance of the Einstein-Cartan action in any dimension
- Constraint structure of the three dimensional massive gravity
- An Analysis of the First Order Form of Gauge Theories
- Darboux coordinates for the Hamiltonian of first order Einstein-Cartan gravity
- Covariant Gauge Fixing and Canonical Quantization
- Canonical Formulation of A Bosonic Matter Field in 1+1 Dimensional Curved Space
- Ghosts from Ghosts in the BRST Formalism
- Algebraic analysis of a model of two-dimensional gravity