Related papers: Projective geometry and special relativity

Superluminal particles are not excluded by particle physics. The apparent Lorentz invariance of the laws of physics does not imply that space-time is indeed minkowskian. Matter made of solutions of Lorentz-invariant equations would feel a…

In this paper, we generalize the usual notions of waves, fronts and propagation speeds in a very general setting. These new notions, which cover all classical situations, involve uniform limits, with respect to the geodesic distance, to a…

I show that the generalized Beltrami differentials and projective connections which appear naturally in induced light cone $W_n$ gravity are geometrical fields parametrizing in one-to-one fashion generalized projective structures on a fixed…

The essence of the method of physics is inseparably connected with the problem of interplay between local and global properties of the universe. In the present paper we discuss this interplay as it is present in three major departments of…

We present the theory of special relativity here through the lens of differential geometry. In particular, we explicitly avoid any reference to hypotheses of the form "The laws of physics take the same form in all inertial reference frames"…

An effective mathematical framework based on Presymplectic Geometry for dealing with the "phase space picture" of timeless dynamics in General Relativity is presented. In General Relativity, the presence of the scalar Hamiltonian constraint…

In the framework of the debate on high-frequency gravitational waves (GWs), after a review of GWs in standard General Relativity, which is due for completness, the possibility of merging such a traditional analysis with the Hyperspace…

The intimate link between complex geometry and the problem of the pre-metric formulation of electromagnetism is explored. In particular, the relationship between 3+1 decompositions of R4 and the decompositions of the vector space of…

In a generalized Heisenberg/Schroedinger picture we use an invariant space-time transformation to describe the motion of a relativistic particle. We discuss the relation with the relativistic mechanics and find that the propagation of the…

Over the last three years, a number of fundamental physical issues were addressed in loop quantum gravity. These include: A statistical mechanical derivation of the horizon entropy, encompassing astrophysically interesting black holes as…

We outline how the symmetry groups of spacetime are interpreted in a gauge-theoretic approach. Specifically, we focus on the hypermomentum concept and discuss the hyperfluid, that appropriately generalizes the perfect (Euler) fluid of…

The four dimensional spacetime continuum, as first conceived by Minkowski, has become the dominant framework within which to describe physical laws. In this paper, we show how this four-dimensional structure is a natural property of…

This thesis covers several developments performed in metric-affine gravity. This alternative framework extends General Relativity by considering a more general connection than the one induced by the metric (i.e., arbitrary torsion and…

Extended Theories of Gravity can be considered a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales. They are an approach that, by preserving the undoubtedly positive results of Einstein's Theory, is…

The equivalence of a conformal metric on 4-dimensional space-time and a local field of 3-dimensional subspaces of the space of 2-forms over space-time is discussed and the basic notion of transection is introduced. Corresponding relation is…

We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry,…

We discuss the notions of circumradius, inradius, diameter, and minimum width in generalized Minkowski spaces (that is, with respect to gauges), i.e., we measure the "size" of a given convex set in a finite-dimensional real vector space…

It is argued that the `problem of time' in quantum gravity necessitates a refinement of the local inertial structure of the world, demanding a replacement of the usual Minkowski line element by a 4+2n dimensional pseudo-Euclidean line…

Generalized geometry provides the framework for a systematic approach to non-symmetric metric gravity theory and naturally leads to an Einstein-Kalb-Ramond gravity theory with totally anti-symmetric contortion. The approach is related to…

In physics, two systems that radically differ at short scales can exhibit strikingly similar macroscopic behaviour: they are part of the same long-distance universality class. Here we apply this viewpoint to geometry and initiate a program…