Unimodular conformal and projective relativity

Unimodular relativity and cosmological constant

Unimodular relativity is a theory of gravity and space–time with a fixed absolute space–time volume element, the modulus, which we suppose is proportional to the number of microscopic modules in that volume element. In general relativity an arbitrary fixed measure can be imposed as a gauge condition, while in unimodular relativity it is determined by the events in the volume. Since this seems t...

Unimodular Elements and Projective Modules

We are mainly concerned with the completablity of unimodular rows to an invertible matrix. We first relate this to stable range of the ring. Further, we consider rows generating an idempotent of the ring to obtain completability under special conditions. We try to obtain analogues of important theorems regarding unimodular rows in the case of these “idempotent rows”. By ring, we shall always me...

Veblen on Projective Relativity 191 Veblen on Projective Relativity

This book by Professor Veblen is a result of a series of lectures given at the University of Göttingen during the summer of 1932. I t deals with that new aspect of the theory of relativity which is often called projective relativity on account of its relation to projective geometry. I t allows a unified theory of the gravitational and the electromagnetic field, and, though it is not referred to...

Space versus Time: Unimodular versus Non-Unimodular Projective Ring Geometries?

Finite projective (lattice) geometries defined over rings instead of fields have recently been recognized to be of great importance for quantum information theory. We believe that there is much more potential hidden in these geometries to be unleashed for physics. There exist specific rings over which the projective spaces feature two principally distinct kinds of basic constituents (points and...

Spinors in Projective Relativity.