Hamiltonian dynamics for Einstein's action in G→\rightarrow0 limit

The Hamiltonian analysis for the Einstein's action in $G\to 0$ limit is performed. Considering the original configuration space without involve the usual $ADM$ variables we show that the version $Gto 0$ for Einstein's action is devoid of physical degrees of freedom. In addition, we will identify the relevant symmetries of the theory such as the extended action, the extended Hamiltonian, the gauge transformations and the algebra of the constraints. As complement part of this work, we develop the covariant canonical formalism where will be constructed a closed and gauge invariant symplectic form. In particular, using the geometric form we will obtain by means of other way the same symmetries that we found using the Hamiltonian analysis

Self-dual action for fermionic fields and gravitation

This paper studies the self-dual Einstein-Dirac theory. A generalization is obtained of the Jacobson-Smolin proof of the equivalence between the self-dual and Palatini purely gravitational actions. Hence one proves equivalence of self-dual Einstein-Dirac theory to the Einstein-Cartan-Sciama-Kibble-Dirac theory. The Bianchi symmetry of the curvature, core of the proof, now contains a non-vanishing torsion. Thus, in the self-dual framework, the extra terms entering the equations of motion with respect to the standard Einstein-Dirac field equations, are neatly associated with torsion

Essential self-adjointness in 1-loop quantum cosmology

The quantization of closed cosmologies makes it necessary to study squared Dirac operators on closed intervals and the corresponding quantum amplitudes. This paper shows that the proof of essential self-adjointness of these second-order elliptic operators is related to Weyl’s limit point criterion, and to the properties of continuous potentials which are positive near zero and are bounded on the interval [1,infty

Boundary terms for massless fermionic fields

Local supersymmetry leads to boundary conditions for fermionic fields in one-loop quantum cosmology involving the Euclidean normal _{e}n_{A}^{; ; A'} to the boundary and a pair of independent spinor fields psi^{A} and {widetilde psi}^{A'}. This paper studies the corresponding classical properties, i.e. the classical boundary-value problem and boundary terms in the variational problem. If sqrt{2} ; {_{e}n_{A}^{; ; A'}} ; psi^{A} mp {widetilde psi}^{A'} equiv Phi^{A'} is set to zero on a 3-sphere bounding flat Euclidean 4-space, the modes of the massless spin-1/2 field multiplying harmonics having positive eigenvalues for the intrinsic 3-dimensional Dirac operator on S^{3} should vanish on S^{3}. Remarkably, this coincides with the property of the classical boundary-value problem when spectral boundary conditions are imposed on S^3 in the massless case. Moreover, the boundary term in the action functional is proportional to the integral on the boundary of Phi^{A'} ; {_{e}n_{AA'}} ; psi^{A}