Causal structure and degenerate phase boundaries

Abstract

Timelike and null hypersurfaces in the degenerate space-times in the Ashtekar theory are defined in the light of the degenerate causal structure proposed by Matschull. Using the new definition of null hypersufaces, the conjecture that the "phase boundary" separating the degenerate space-time region from the non-degenerate one in Ashtekar's gravity is always null is proved under certain circumstances.Comment: 13 pages, Revte

Hamiltonian Analysis of 3-Dimensional Connection Dynamics in Bondi-like Coordinates

“…It is very different from the Hamiltonian analysis of gravitational theory in the literatures. Although the Hamiltonian analysis in the Ashtekar formalism permits the degenerate geometry [15,16,17], the non-degenerated geometry is mainly concerned. However, what is degenerate in the formalism is just the induced geometry on each slice, while the 3-dimensional geometry is still non-degenerate.…”

“…As a result, the geometries on the slices are always degenerate though the geometries for the spacetime are not degenerate. This is very different from the ADM formalism in which only non-degenerate geometries on slices are dealt with [1], [2] and from the Ashtekar formalism in which non-degenerate geometries on slices are mainly concerned though the degenerate geometries may be studied as well [15], [16], [17].…”

Towards the self-adjointness of a Hamiltonian operator in loop quantum gravity

“…The phase space of the classical Ashtekar theory contains points characterized by the lower than 3 rank of the frame. Mathematically, they are regular and make perfect sense [44,45]. In particular, the rank 2 case is exactly soluble for the vacuum theory [46].…”

A minimal see-saw model for hierarchical neutrino masses with large mixing

“…in the context of the atmospheric and solar neutrino oscillations. I shall concentrate on the simpler of the two models [8], corresponding to the gauge charge (10). Indeed it seems to represent a minimal see-saw model for explaining these neutrino oscillation data.…”

“…where D is the 2 × 3 Dirac mass matrix at the bottom left of (17). One can then calculate the corresponding mass eigen-values m 1,2,3 and mixing-angles by diagonalising this matrix [8]. Alternatively we can read off the approximate magnitudes of these quantities directly from the mass matrix (17), i.e.…”