Related papers: Towards Spectral Geometry for Causal Sets
A very small dispersion in the speed of light may be observable in Fermi time- and energy-tagged data on variable sources, such as gamma-ray bursts (GRB) and active galactic nuclei (AGN). We describe a method to compute the size of this…
A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of…
The well-known physical equivalence drawn from hole theory is applied in this article. The author suggests to replace, in the part of Feynman diagram which cannot be fixed by experiments, each fermion field operator, and hence fermion…
We propose, for dimension d, a discrete Lorentz invariant operator on scalar fields that approximates the Minkowski spacetime scalar d'Alembertian. For each dimension, this gives rise to a scalar curvature estimator for causal sets, and…
A distance measure is presented between two unitary propagators of quantum systems of differing dimensions along with a corresponding method of computation. A typical application is to compare the propagator of the actual (real) process…
We link the notion causality with the orientation of the 2-complex on which spin foam models are based. We show that all current spin foam models are orientation-independent, pointing out the mathematical structure behind this independence.…
Causal investigations in observational studies pose a great challenge in research where randomized trials or intervention-based studies are not feasible. We develop an information geometric causal discovery and inference framework of…
We seek a practical method for establishing dense correspondences between two images with similar content, but possibly different 3D scenes. One of the challenges in designing such a system is the local scale differences of objects…
Inspired by recent developments in the study of chaos in many-body systems, we construct a measure of local information spreading for a stochastic Cellular Automaton in the form of a spatiotemporally resolved Hamming distance. This…
Feynman's i-epsilon prescription for quantum field theoretic propagators has a quite natural reinterpretation in terms of a slight complex deformation of the Minkowski spacetime metric. Though originally a strictly flat-space result, once…
We discuss contact invariant structures on the space of solutions of a third-order ordinary differential equation. Associated to any third-order differential equation modulo contact transformations, Chern introduced a degenerate conformal…
By appeal to Distribution Theory we discuss in rigorous fashion, without appealing to {\bf any conjecture} (as usually done by other authors), the boundary-bulk propagators for the scalar field, both in the non-massive and massive cases.…
Feynman amplitudes in perturbation theory form the basis for most predictions in particle collider experiments. The mathematical quantities which occur as amplitudes include values of the Riemann zeta function and relate to fundamental…
This study shows how Aronszajn's theory of reproducing kernels can be of use for the construction the Hilbert spaces of quantum theory. We show that the Feynman propagator is an example of a reproducing kernel under a boundedness condition.…
Light propagation through a normal medium is determined not only by the real part of the refractive index but also by its imaginary part, which represents optical gain and loss. Therefore, two media with different gain and loss landscapes…
We model the classical transmission of a massless scalar field from a source to a detector on a background causal set. The predictions do not differ significantly from those of the continuum. Thus, introducing an intrinsic inexactitude to…
A good generalization of the Euclidean dimension to disordered systems and non crystalline structures is commonly required to be related to large scale geometry and it is expected to be independent of local geometrical modifications. The…
We first introduce a class of divergence measures between power spectral density matrices. These are derived by comparing the suitability of different models in the context of optimal prediction. Distances between "infinitesimally close"…
We present significant evidence that the powerful property of Yangian invariance extends to a new large class of conformally invariant Feynman integrals. Our results apply to planar Feynman diagrams in any spacetime dimension dual to an…
Visual representations underlie object recognition tasks, but they often contain both robust and non-robust features. Our main observation is that image classifiers may perform poorly on out-of-distribution samples because spurious…