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A possible model for quantum kinematics of a test particle in a curved space-time is proposed. Every reasonable neighbourhood V_e of a curved space-time can be equipped with a nonassociative binary operation called the geodesic…
Some concepts of real and complex projective geometry are applied to the fundamental physical notions that relate to Minkowski space and the Lorentz group. In particular, it is shown that the transition from an infinite speed of propagation…
In pregeometry a metric arises as a composite object at large distances. We investigate if its signature, which distinguishes between time and space, could be a result of the dynamics rather than being built in already in the formulation of…
An effective theory of gravity in the infrared is proposed, which involves the determinant of the metric relative to the determinant of a prior metric taken to be that of Minkowski spacetime. This effective theory can be interpreted as a…
We investigate a quantum geometric space in the context of what could be considered an emerging effective theory from Quantum Gravity. Specifically we consider a two-parameter class of twisted Poincar\'e algebras, from which Lie-algebraic…
In this paper, we present the results of our investigation relating particle dynamics and non-commutativity of space-time by using Dirac's constraint analysis. In this study, we re-parameterise the time $t=t(\tau)$ along with $x=x(\tau)$…
We investigate the asymptotic structure of electromagnetism in Minkowski space in even and odd spacetime dimensions $\geq 4$. We focus on $d>4$ since the case $d=4$ has been studied previously at length. We first consider spatial infinity…
With approaching quantum/noncommutative models for the deep microscopic spacetime in mind, and inspired by our recent picture of the (projective) Hilbert space as the model of physical space behind basic quantum mechanics, we reformulate…
The main objective consists in endowing the elementary particles with an algebraic space-time structure in the perspective of unifying quantum field theory and general relativity: this is realized in the frame of the Langlands global…
A phenomenology for the deep spatial geometry of loop quantum gravity is introduced. In the context of a simple model, an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to…
In the study of the electronic structure of heavy atoms, relativistic effects cannot be neglected and the Dirac operator naturally appears in place of the Schr\"odinger operator, raising a number of additional difficulties. The complexity…
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum…
This article is an interdisciplinary review and an on-going progress report over the last few years made by myself and collaborators in certain fundamental subjects on two major theoretic branches in mathematics and theoretical physics:…
Quantum theory and relativity are the pillar theories on which our understanding of physics is based. Poincar\'e invariance is a fundamental physical principle stating that the experimental results must be the same in all inertial reference…
The absence of Birkhoff's theorem in effective quantum gravity models leads to a fundamental ambiguity in the vacuum sector, where a priori no unique vacuum solution exists. As a result, phenomenological investigations of the physical…
We use the loop-by-loop Baikov representation to investigate the geometries in Feynman integrals contributing to the classical dynamics of a black-hole two-body system in the post-Minkowskian expansion of general relativity. These…
The physical phase space in gauge systems is studied. Effects caused by a non-Euclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac…
We introduce canonical coordinates on minimal time-like surfaces in the n-dimensional Minkowski space and prove the existence and the uniqueness of these parameters. With respect to these coordinates the coefficients of the first…
This explanatory note, based on the geometrical method by Kijovski and Tulczyjew, describes the construction of the reduced phase space of Lagrangian field theories, i.e., the correct space of initial conditions with its symplectic…
The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic…