Related papers: A characterization of causal automorphisms by wave…
The well-known fact that classical automorphisms of (compactified) Minkowski spacetime (Poincare or conformal trandsformations) also allow a natural derivation/interpretation in the modular setting (in the operator-algebraic sense of Tomita…
The formulae of special relativity are developed through the k-calculus with no presumption of a manifold. The metric is determined empirically by the exchange of photons, and the treatment suggests that the exchange of photons seen in…
The first part of my thesis lays the foundations to generalized Lorentz geometry. The basic algebraic structure of finite-dimensional modules over the ring of generalized numbers is investigated. The motivation for this part of my thesis…
In this paper, we establish equiform differential geometry of space and timelike curves in 4-dimensional Minkowski space. We obtain some conditions for these curves. Also, general helices with respect to their equiform curvatures are…
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…
In our model of quantum gravity the quantum development of a Cauchy hypersurface is governed by a wave equation derived as the result of a canonical quantization process. To find physically interesting solutions of the wave equation we…
A mathematical definition of classical causality over discrete spacetime dynamics is formulated. The approach is background free and permits a definition of causality in a precise way whenever the spacetime dynamics permits. It gives a…
The nature of cosmic time is illuminated using Hamilton-Jacobi theory for general relativity. For problems of interest to cosmology, one may solve for the phase of the wavefunctional by using a line integral in superspace. Each contour of…
Replacing 4D Minkowski space by 5D canonical space leads to a clearer derivation of the main features of wave mechanics, including the wave function and the velocity of de Broglie waves. Recent tests of wave-particle duality could be…
Some results from arguments of research dealt with R. Raczka are exposed and extended. In particular new arguments are brought in favor of the conjecture, formulated with him, that both space-time and momentum may be conformally…
In this paper we study the structure of the manifold of solitary waves in some deformations of SO(2) symmetric two-component scalar field theoretical models in two-dimensional Minkowski space. The deformation is chosen in order to make the…
The dynamics of spinorial wave functions in a causal fermion system is studied. A so-called dynamical wave equation is derived. Its solutions form a Hilbert space, whose scalar product is represented by a conserved surface layer integral.…
Quantum mechanical operators and quantum fields are interpreted as realizations of timespace manifolds. Such causal manifolds are parametrized by the classes of the positive unitary operations in all complex operations, i.e. by the…
We examine the dependence of quantization on global properties of a classical system. Quantization based on local properties may lead to ambiguities and inconsistency between local and global symmetries of a quantum system. Our quantization…
The causality structure of two-dimensional manifolds with degenerate metrics is analysed in terms of global solutions of the massless wave equation. Certain novel features emerge. Despite the absence of a traditional Lorentzian Cauchy…
For a physical interpretation of a theory of quantum gravity, it is necessary to recover classical spacetime, at least approximately. However, quantum gravity may eventually provide classical spacetimes by giving spectral data similar to…
A complete classification of space-time models is presented, which admit the privileged coordinate systems, where the Hamilton-Jacobi equation for a test particle is integrated by the method of complete separation of variables with…
We study time-dependent acoustic and electromagnetic waves governed by the scalar wave equation or Maxwell's equations in a bounded three-dimensional domain. We establish the existence of time-dependent boundary excitations that can be…
In the present contribution we show that the introduction of a conserved axial current in electrodynamics can explain the quantization of electric charge, inducing at the same time a dynamical quantization of spacetime.
General relativity allows solutions exhibiting closed timelike curves. Time travel generates paradoxes and quantum mechanics generalizations were proposed to solve those paradoxes. The implications of self-consistent interactions on acausal…