Fermion Systems in Discrete Space-Time Exemplifying the Spontaneous Generation of a Causal Structure

As toy models for space-time on the Planck scale, we consider examples of fermion systems in discrete space-time which are composed of one or two particles defined on two up to nine space-time points. We study the self-organization of the particles as described by a variational principle both analytically and numerically. We find an effect of spontaneous symmetry breaking which leads to the emergence of a discrete causal structure.Comment: 37 pages, LaTeX, 12 figures, minor changes (published version

Inversion of the conical Radon transform with vertices on a surface of revolution arising in an application of a Compton camera

A Compton camera has been introduced for use in single photon emission computed tomography to improve the low efficiency of a conventional gamma camera. In general, a Compton camera brings about the conical Radon transform. Here we consider a conical Radon transform with the vertices on a rotation symmetric set with respect to a coordinate axis. We show that this conical Radon transform can be decomposed into two transforms: the spherical sectional transform and the weighted fan beam transform. After finding inversion formulas for these two transforms, we provide an inversion formula for the conical Radon transform.clos