相关论文: Symplectic vs pseudo-orthogonal structure of space…

It is conjectured that the symplectic structure of space-time is superior to the metric one. Instead of the commonly adopted pseudo-orthogonal groups SO(1,d-1), d\ge4, the complex symplectic ones Sp(2l,C), l\ge1 are proposed as the local…

It is conjectured that in the origin of space-time there lies a symplectic rather than metric structure. The complex symplectic symmetry Sp(2l,C), l\ge1 instead of the pseudo-orthogonal one SO(1,d-1), d\ge4 is proposed as the space-time…

The aim of this note is to present a construction of symplectic structures on orientable globally hyperbolic 4-dimensional lorentzian manifolds. Said structures are defined on the manifold itself, not on its cotangent bundle. It also…

We provide five rearticulations of the thesis that the structure of spacetime is conventional, rather than empirically determined, based upon variation of the structures that are empirically underdetermined and modal contexts in which this…

A physical interpretation of axioms of the differential structure of space-time is presented. Consequences of such interpretation for cosmic string's space-time with a scalar field are studied. It is shown that the assumption of smoothness…

We give a general and nontechnical review of some aspects of noncommutative geometry as a tool to understand the structure of spacetime. We discuss the motivations for the constructions of a noncommutative geometry, and the passage from…

A logical model of spatiotemporal structures is pictured as a succession of processes in time. One usual way to formalize time structure is to assume the global existence of time points and then collect some of them to form time intervals…

This paper presents a space-time-wise orthogonal analysis of space-time crystals. This analysis provides a solution consisting of a pair of explicit parametric equations that result from a separate application of the Bloch-Floquet theorem…

The causal structure of space-time offers a natural notion of an opposite or orthogonal in the logical sense, where the opposite of a set is formed by all points non time-like related with it. We show that for a general space-time the…

We realize the hamiltonian action of the one spatial Poincare group G, analogous to the projective unitary representation, on a coadjoint orbit of G whic we interpret as a symplectic space-time where the time is associated to a physical…

It seems to be a common belief that the space in which we live is a space-time manifold of dimension at least four. In the present article we wish to draw attention to a slightly different possibility - a space-time pseudomanifold (or even…

Why is the manifold topology in a spacetime taken for granted? Why do we prefer to use Riemann open balls as basic-open sets, while there also exists a Lorentz metric? Which topology is a best candidate for a spacetime; a topology…

In this letter we briefly investigate the mathematical structure of space-time in the framework of discretization. It is shown that the discreteness of space-time may result in a new mechanical system which differ from the usual quantum…

Popular wisdom amongst theoretical physicists says that the continuum structure of spacetime is probably not elementary, but rather emergent. While many arguments to support that view arise from speculative ideas, the argument can also be…

The dimensional structure of space-time is investigated according to physical and mathematical methods. We show that ther are various empirical and theoretical restrictions on the number of independent dimensions of space-time, consequently…

I examine the debate between substantivalists and relationalists about the ontological character of spacetime and conclude it is not well posed. I argue that the so-called Hole Argument does not bear on the debate, because it provides no…

Normed division and Clifford algebras have been extensively used in the past as a mathematical framework to accommodate the structures of the standard model and grand unified theories. Less discussed has been the question of why such…

We provide a simple proof that conformally semi-symmetric spacetimes are actually semi-symmetric. We also present a complete refined classification of the semi-symmetric spacetimes.

A general relativistic description of a disk rotating at constant angular velocity is given. It is argued that conceptually this direct approach poses fewer problems than the special relativistic one. For observers on the disk, the geometry…

Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…