Related papers: Spacetime models, fundamental interactions and non…
The usual quantization of a classical space-time field does not touch the non-geometrical character of quantum mechanics. We believe that the deep problems of unification of general relativity and quantum mechanics are rooted in this poor…
In five dimensional cosmological models, the convention is to include the fifth dimension in a way similar to the other space dimensions. In this work we attempt to introduce the fifth dimension in a way that a time dimension would be…
We construct a simple toy model of a closed FLRW spacetime by starting from a flat five dimensional scalar field space. The action contains no curvature terms. A string-like potential is used for the field space. The model is fully…
We argue that special and general theories of relativity implicitly assume spacetime events correspond to quantum measurement outcomes. This leads to a change in how one should view the equivalence of spacetime and gravity. We describe a…
The usual formulation of time-dependent mechanics implies a given splitting $Y=R\times M$ of an event space $Y$. This splitting, however, is broken by any time-dependent transformation, including transformations between inertial frames. The…
We illustrate a physical situation in which topological symmetry, its breakdown, space-time uncertainty principle, and background independence may play an important role in constructing and understanding matrix models. First, we show that…
We introduce three space-times that are discrete in time and compatible with the Lorentz symmetry. We show that these spaces are no commutative, with commutation relations similar to the relations of the Snyder and Yang spaces. Furthermore,…
The newest model for space-time is based on sub-Riemannian geometry. In this paper, we use a combination of Lorentzian and sub-Riemannian geometry, the suggest a new model which likes to its ancestors, but with the most efficient in…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
Using very weak criteria for what may constitute a noncommutative geometry, I show that a pseudo-Riemannian manifold can only be smoothly deformed into noncommutative geometries if certain geometric obstructions vanish. These obstructions…
A model with a scalar type eight-fermion interaction is investigated in curved spacetime. The ground state of the model can be obtained by observing the effective potential. Applying the Riemann normal coordinate expansion, we calculate an…
Geometrical analysis of a new type of Unified Field Theoretical models follow the guidelines of previous works of the authors is presented. These new unified theoretical models are characterized by an underlying hypercomplex structure, zero…
With the aid of a Fermi-Walker chart associated with an orthonormal frame attached to a time-like curve in spacetime, a discussion is given of relativistic balance laws that may be used to construct models of massive particles with spin,…
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…
This paper is the second part of a series that develops the mathematical framework necessary for studying field theories on ``T-Minkowski'' noncommutative spacetimes. These spacetimes constitute a class of noncommutative geometries,…
We study the geometry of a two-sheeted space-time within the framework of non-commutative geometry. As a prelude to the Standard Model in curved space-time, we present a model of a left- and a right- chiral field living on the two…
We use a result of Hawking and Gilkey to define a Euclidean path integral of gravity and matter which has the special property of being independent of the choice of basis in the space of fields. This property allows the path integral to…
Spacetime emergence refers to the notion that classical spacetime "emerges" as an approximate macroscopic entity from a non-spatio-temporal structure present in a more complete theory of interacting fundamental constituents. In this…
Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures…
The geodesic deviation equation (`GDE') provides an elegant tool to investigate the timelike, null and spacelike structure of spacetime geometries. Here we employ the GDE to review these structures within the…