Related papers: Relational Quadrilateralland. I. The Classical The…

It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally "curved" space-time. This shows that it is possible to formulate quantum…

General Relativity on closed spatial topologies can be derived, using a technique called "best-matching", as an evolving 3-geometry subject to constraints. These constraints can be thought of as a way of imposing temporal and spatial…

Relational particle dynamics include the dynamics of pure shape and cases in which absolute scale or absolute rotation are additionally meaningful. These are interesting as regards the absolute versus relative motion debate as well as…

The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…

We present a quantum model for the motion of N point particles, implying nonlocal (i.e., superluminal) influences of external fields on the trajectories, that is nonetheless fully relativistic. In contrast to other models that have been…

A local resolution to the Problem of Time that is Machian and was previously demonstrated for various relational mechanics models is here shown to work for a more widely studied quantum cosmological model. Namely, closed isotropic…

Absolute space is eliminated from the body of mechanics by gauging translations and rotations in the Lagrangian of a classical system. The procedure implies the addition of compensating terms to the kinetic energy, in such a way that the…

In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a non-trivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are…

Because of the non-locality of quantum entanglement, realist approaches to completing quantum mechanics have implications for our conception of space. Quantum gravity also is expected to predict phenomena in which the locality of classical…

A consistent description of the fundamental interactions of particle physics based upon the assumption of 6 real extra dimensions is presented. The usual 4-dimension space-time, a curved hypersurface with the Lorentz group as local…

The Problem of Time in Quantum Gravity is analyzed from a classical presymplectic perspective. In the first part of the paper the Three Space Approach to General Relativity is introduced via the Barbour-Foster-\'O Murchadha action and the…

To solve the quantum-mechanical problem the procedure of mapping onto linear space $W$ of generators of the (sub)group violated by given classical trajectory is formulated. The formalism is illustrated by the plane H-atom model. The problem…

Relationalism -- along the lines developed by Barbour and collaborators in the past 3 decades -- can be considered an advance with 1/4 of the facets of the canonical approach's Problem of Time as identified by Isham and Kuchar. Indeed,…

Many questions about triangles and quadrilaterals with rational sides, diagonals and areas can be reduced to solving certain Diophantine equations. We look at a number of such questions including the question of approximating arbitrary…

With toy modelling of conceptual aspects of quantum cosmology and the problem of time in quantum gravity in mind, I study the classical and quantum dynamics of the pure-shape (i.e. scale-free) triangle formed by 3 particles in 2-d. I do so…

A central aim of theoretical physics is to account for the structure of matter at the most elementary level as underlying the Standard Model of particle physics, and ideally also as a basis for a substantial dark sector, as distributed in…

This thesis is devoted to studying various aspects of quantum mechanics on non-commutative space-time and to capture some of the surviving aspects of symmetries of quantum field theory on such space-time, illustrated through toy models in…

The physical world is quantum. However, our description of the quantum physics still relies much on concepts in classical physics and in some cases with `quantized' interpretations. The most important case example is that of spacetime. We…

We construct the action of a relativistic spinning particle from a non-linear realization of a space-time odd vector extension of the Poincar\'e group. For particular values of the parameters appearing in the lagrangian the model has a…

The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…