Minkowski Pythagorean hodograph curves are polynomial curves with polynomial speed, measured with respect to Minkowski norm. Curves of this special class are particularly well suited for representing medial axis transforms of planar domains. In the present paper we generalize this polynomial class to a rational class of curves in Minkowski 3-space. We show that any rational Minkowski Pythagorea...

For the closed relativistic string carrying a pointlike mass the exact solutions of the dynamical equations are obtained and studied. These solutions describe states of the mentioned system moving in Minkowski space and also in the space that is the direct product of Minkowski space and a compact manifold (torus). We consider the closed relativistic string with one massive point (homeomorphic t...

In this paper we have studied the nature of kinematical and dynamical laws in κ-Minkowski spacetime from a new perspective: the canonical phase space approach. We have introduced a new form of κ-Minkowski phase space algebra from which we recover the κ-extended finite Lorentz transformations derived in [13]. This is a particular form of a Deformed Special Relativity model that admits a modified...

It is claimed in another paper that the collapse of a quantum mechanical wave function is more than invariant, it is trans-representational. It must occur along a fully invariant surface. The obvious surface available for this purpose is that of the backward time cone of the collapse event as proposed by Hellwig and Kraus. This collapse is widely believed to result in paradoxical causal loops t...

The author has proposed five rules that permit conscious observers to be included in quantum mechanics. In the present paper, these rules are applied to the observation of a non-local pair of correlated particles. Rule (4) again prevents an anomalous result. Two different kinds of relativistic state reduction are considered, where these differ in the way that they impose boundary conditions in ...

We discuss the concept of the bisector of a segment in a Minkowski normed n-space. We prove that all bisectors are topological images of a plane of the embedding Euclidean 3-space iff the shadow boundaries of the unit ball K are topological circles. To a conjectured proving strategy for dimensions n, we introduce the concept of general parameter sphere of the unit ballK, corresponding to a dire...

A prescription is given for performing numerical simulations of field theory in Minkowski space using the Langevin equation. By introducing a weak damping term we find that the Langevin equations relax to their equilibrium values in a rather modest amount of time. As an example, we calculate the Green functions for both the harmonic and anharmonic oscillators. We study both analytically and num...

We construct a model of Brownian motion in Minkowski space. There are two aspects of the problem. The first is to define a sequence of stopping times associated with the Brownian “kicks” or impulses. The second is to define the dynamics of the particle along geodesics in between the Brownian kicks. When these two aspects are taken together, the Central Limit Theorem (CLT) leads to temperature d...

Let p1, . . . ,pk be k points (events) in (n+1)-dimensional Minkowski space R. Using the theory of hyperplane arrangments and chromatic polynomials, we obtain information on the number of different orders in which the events can occur in different reference frames if the events are sufficiently generic. We consider the question of what sets of orderings of the points are possible and show a con...

We describe a set of periodic lattices in 1+1 -dimensional Minkowski space, where each lattice has an associated symmetry group consisting of inhomogeneous Lorentz transformations that map the lattice onto itself. Our results show how ideas of crystal structure in Euclidean space generalize to Minkowski space and provide an example that illustrates basic concepts of spacetime symmetry. © 2010 A...