Related papers: On the Relativity in Configuration Space: A Renewe…
The personal spatial structure of an observer is introduced as a central element in the positioning of objects in space. The link between a reference frame used by an observer and his personal spatial structure is discussed. Research on…
The concept of supersymmetry in a quantum mechanical system is extended, permitting the recognition of many more supersymmetric systems, including very familiar ones such as the free particle. Its spectrum is shown to be supersymmetric,…
In this paper we review some aspects of relativistic particles' mechanics in the case of a non-trivial geometry of momentum space. We start with showing how the curved momentum space arises in the theory of gravity in 2+1 dimensions coupled…
We claim that both multipartiteness and localization of subsystems of compound quantum systems are of an essentially relative nature crucially depending on the set of operationalistically available states. In a more general setting, to…
Brane-Universe model embedded in 6-dimensional space-time with the signature (2+4) is considered. A matter is gravitationally trapped in three space dimensions, but both time-like directions are open. Choosing of the dimension and the…
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 survey indications from different branches of Physics that the fine scale structure of spacetime is not adequately described by a manifold. Based on the hints we accumulate, we propose a new structure, which we call a quantum topos. In…
A quantum version of the action principle in a simple covariant dynamical theory of two relativistic particles is formulated. The central object of this new formulation of quantum theory is a stationary eigenvalue of the quantum action.…
We describe a theory amalgamating quantum theory and general relativity through the identification of a continuous 4-dimensional spacetime arena constructed from the substructures of a generalised multi-dimensional form for proper time. In…
We study the action and the dynamics of a relativistic particle, uncharged or charged, in multiscale spacetimes. Invariance under reparametrizations and Poincar\'e symmetries uniquely determine the action and the line element to be the…
Here we will discuss the philosophical differences between an approach to the deep nature of physical space based on the concept of coordinates and one based on the concept of relation. The philosophical superiority of the second approach…
We will highlight that despite there being various approaches to quantum gravity, there are universal approach-independent features of quantum gravity. The geometry of spacetime becomes an emergent structure, which emerges from some purely…
We construct matter field theories in ``theory space'' that are fractal, and invariant under geometrical renormalization group (RG) transformations. We treat in detail complex scalars, and discuss issues related to fermions, chirality, and…
This paper studies the configuration space of all possible positions of a linkage in R^n. For example, it shows that for every compact algebraic set, there is a linkage whose configuration space is analytically isomorphic to a finite number…
We consider dynamics of massless particle in 2d spacetimes with constant curvature. We analyze different examples of spacetime. Dynamical integrals are constructed from spacetime symmetry related to $sl(2.{\bf R})$ algebra. Mass-shell…
The four dimensional spacetime continuum, as first conceived by Minkowski, has become the dominant framework within which to describe physical laws. In this paper, we show how this four-dimensional structure is a natural property of…
We present here a set of lecture notes on quantum systems with time-dependent boundaries. In particular, we analyze the dynamics of a non-relativistic particle in a bounded domain of physical space, when the boundaries are moving or…
In usual quantum theory, the information available about a quantum system is defined in terms of the density matrix describing it on a spacelike surface. This definition must be generalized for extensions of quantum theory which do not have…
It is well known that gravity in 2+1 dimensions can be recast as Chern-Simons theory, with the gauge group given by the local isometry group, depending on the metric signature and the cosmological constant. Point particles are added into…
Central configurations play an important role in the dynamics of the $n$-body problem: they occur as relative equilibria and as asymptotic configurations in colliding trajectories. We illustrate how they can be found as projective fixed…