We expand on the idea that spacetime signature should be treated as a dy-namical degree of freedom in quantum field theory. It has been argued that the probability distribution for signature, induced by massless free fields, is peaked at the Lorentzian value uniquely in D=4 dimensions. This argument is reviewed, and certain consistency constraints on the generalized signature (i.e. the tangent ...

We present an atomic prism spectrometer that utilizes the steep linear dispersion between two strongly absorbing hyperfine resonances of rubidium. We resolve spectral lines 50 MHz apart and, utilizing a larger part of the available spectrum than only between the two resonances, we spatially separate collinear pump, signal, and idler beams resulting from a four-wave mixing process. Due to the hi...

Helfer in [6] was the first to produce an example of a spacelike Lorentzian geodesic with a continuum of conjugate points. In this paper we show the following result: given an interval [a, b] of IR and any closed subset F of IR contained in ]a, b], then there exists a Lorentzian manifold (M, g) and a spacelike geodesic γ : [a, b] → M such that γ(t) is conjugate to γ(a) along γ iff t ∈ F .

We consider a system of globally coupled active rotators near the excitable regime. The system displays a transition to a state of collective firing induced by disorder. We show that this transition is found generically for any diversity distribution with well-defined moments. Singularly, for the Lorentzian distribution (widely used in Kuramoto-like systems) the transition is not present. This ...

We apply the “consistent discretization” technique to the Regge action for (Euclidean and Lorentzian) general relativity in arbitrary number of dimensions. The result is a well defined canonical theory that is free of constraints and where the dynamics is implemented as a canonical transformation. In the Lorentzian case, the framework appears to be naturally free of the “spikes” that plague tra...

Quantum energy inequalities (QEIs) were established by Flanagan for the massless scalar field on two-dimensional Lorentzian spacetimes globally conformal to Minkowski space. We extend his result to all two-dimensional globally hyperbolic Lorentzian spacetimes and use it to show that flat spacetime QEIs give a good approximation to the curved spacetime results on sampling timescales short in com...

We study an anisotropic simplicial minisuperspace model with a cosmological constant and a massive scalar field. After obtaining the classical solutions we then compute the semiclassical approximation of the no-boundary wave function of the Universe along a steepest descents contour passing through classical Lorentzian solutions. The oscillatory behaviour of the resulting wave funtion is consis...

2+1 gravity for spacetimes with topology R × T has been much studied. We add a description of how to extend these spacetimes across a Cauchy horizon into a region where the torus becomes Lorentzian. The result is a one parameter family of tori given by a geodesic in the ”Teichmüller space” of Lorentzian tori. We describe this in detail. We also point out that if the modular group is regarded as...

A well-defined regularized path integral for Lorentzian quantum gravity in three and four dimensions is constructed, given in terms of a sum over dynamically triangulated causal space-times. Each Lorentzian geometry and its associated action have a unique Wick rotation to the Euclidean sector. All space-time histories possess a distinguished notion of a discrete proper time. For finite lattice ...

Exponential spectra have been observed in the edges of tokamaks, stellarators, helical devices and linear machines. The observation of exponential power spectra is significant because such a spectral character has been closely associated with the phenomenon of deterministic chaos by the nonlinear dynamics community. The proximate cause of exponential power spectra in both magnetized plasma edge...