Related papers: Two-dimensional Minkowski causal automorphisms and…
This article describes the symmetries of plane wave spacetimes in dimension four and greater. It begins with a description of the isometric automorphisms, and in particular the homogeneous plane waves. Then the article turns to describing…
The acceleration transformations form a 4-parameter Abelian subgroup of the conformal group of Minkowski spacetime. The passive interpretation of acceleration transformations leads to a congruence of uniformly accelerated observers in…
We study quantum causal structures in $1+1$ $\kappa$-Minkowski space-time described by a Lorentzian Spectral Triple whose Dirac operator is built from a natural set of twisted derivations of the $\kappa$-Poincar\'e algebra. We show that the…
In special relativity, the definition of coordinate systems adapted to generic accelerated observers is a long-standing problem, which has found unequivocal solutions only for the simplest motions. We show that the Marzke-Wheeler…
The Groups of causal and conformal automorphisms of globally hyperbolic spacetimes were studied. In two dimensions, we prove that all globally hyperbolic spacetimes that are directed and connected are causally isomorphic. We work out the…
Minkowski space serves as a framework for the theoretical constructions that deal with manifestations of relativistic effects in physical phenomena. But neither Minkowski himself nor the subsequent developers of the relativity theory have…
We describe space-time using split octonions over the reals and use their group of automorphisms, the non-compact form of Cartan's exceptional Lie group G2, as the main geometrical group of the model. Connections of the G2-rotations of…
Loop corrections to unequal-time correlation functions in Minkowski spacetime exhibit secular growth due to a breakdown of time-dependent perturbation theory. This is analogous to secular growth in equal-time correlators on time-dependent…
Aleksandrov, and then Zeeman, showed that the causal relations among the set of points in a Minkowski space of dimension greater than 2 determine the Minkowski space structure of the set up to a global conformal factor. We show that in any…
The worldline of a uniformly accelerated localized observer in Minkowski space is restricted in the Rindler wedge, where the observer can in principle arrange experiments repeatedly, and the Cauchy problem for quantum fields in that Rindler…
We study a two-dimensional dilaton gravity model related by a conformal transformation of the metric to the Callan-Giddings-Harvey-Strominger model. We find that most of the features and problems of the latter can be simply understood in…
We consider Minkowski spacetime, the set of all point-events of spacetime under the relation of causal accessibility. That is, ${\sf x}$ can access ${\sf y}$ if an electromagnetic or (slower than light) mechanical signal could be sent from…
We give a closed expression for the Minkowski (1+1)-dimensional metric in the radar coordinates of an arbitrary non-inertial observer O in terms of O's proper acceleration. Knowledge of the metric allows the non-inertial observer to perform…
The $\kappa$-Minkoswki space-time provides a quantum noncommutative-deformation of the usual Minkowski space-time. However, a notion of causality is difficult to be defined in such a space with noncommutative time. In this paper, we define…
I present a way to visualize the concept of curved spacetime. The result is a curved surface with local coordinate systems (Minkowski Systems) living on it, giving the local directions of space and time. Relative to these systems, special…
We begin from the generalised eight-dimensional Minkowski spacetime structure, previously developed in Clifford geometric algebra $ C\ell(\Re^3) $. We propose that this is the correct algebraic representation for physical three-dimensional…
We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard…
We study the Minkowski formula of conformal Killing-Yano two-forms in a spacetime of constant curvature. We establish the spacetime Alexandrov theorem with a free boundary.
We construct a duality between several simple physical systems by showing that they are different aspects of the same quantum theory. Examples include the free relativistic massless particle and the hydrogen atom in any number of…
For over a century Minkowskian spacetime has dominated discussions of space contraction and time dilation within special relativity. Brown and Pooley have called into question both the assumptions of Minkowski and the effects his presumed…