0 M ay 2 00 2 Space - Time , General Covariance , Dirac - Bergmann Observables and Non - Inertial Frames

qc / 0 10 50 84 v 1 2 3 M ay 2 00 1 Dirac ’ s Observables for the Rest - Frame Instant Form of Tetrad

General Covariance and Its Implications for Einstein's Space-times

This is a review of the chrono-geometrical structure of special and general relativity with a special emphasis on the role of non-inertial frames and of the conventions for the synchronization of distant clocks. ADM canonical metric and tetrad gravity are analyzed in a class of space-times suitable to incorporate particle physics by using Dirac theory of constraints, which allows to arrive at a...

From Einstein’s Hole Argument to Dirac and Bergmann Observables

The individuation of point-events and the Hamiltonian way of distinguishing gravitational from inertial effects in general relativity are discussed. The fact that both particle physics and all the approaches to gravity make use of variational principles employing singular Lagrangians [1] has the consequence that the EulerLagrange equations cannot be put in normal form, some of them may be non i...

ar X iv : 0 70 5 . 07 12 v 2 [ m at h - ph ] 9 M ay 2 00 7 REFLECTION POSITIVITY AND MONOTONICITY

We prove general reflection positivity results for both scalar fields and Dirac fields on a Riemannian manifold, and comment on applications to quantum field theory. As another application, we prove the inequality C D ≤ C N between Dirichlet and Neumann covariance operators on a manifold with a reflection.

0 M ay 2 00 5 Local Stationarity for Lattice Dynamics in the Harmonic Approximation

We consider the lattice dynamics in the harmonic approximation for a simple hypercubic lattice with arbitrary unit cell. The initial data are random according to a probability measure which enforces slow spatial variation on the linear scale ε−1 . We establish two time regimes. For times of order ε−γ , 0 < γ < 1 , locally the measure converges to a Gaussian measure which is space-time stationar...