Related papers: Field-Particle Dynamics in Spacetime Geometries
We generalize and unify the $f(R,T)$ and $f(R,L_m)$ type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$, of the trace of the energy-momentum tensor $T$, and of the…
We propose general guidelines in order to incorporate the geometrical description of gravity in quantum field theory and address the problem of UV divergences non-perturbatively. In our aproach, each virtual particle in a Feynman graph…
We discuss the symmetry properties of the reparametrization invariant model of an interacting relativistic particle where the electromagnetic field is taken as the constant background field. The direct coupling between the relativistic…
Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric problems with a direct motivation in Relativity and other…
We consider a gravitational model in which matter is non-minimally coupled to geometry, with the effective Lagrangian of the gravitational field being given by an arbitrary function of the Ricci scalar, the trace of the matter…
The analogy between dynamics and optics had a great influence on the development of the foundations of classical and quantum mechanics. We take this analogy one step further and investigate the validity of Fermat's principle in…
We investigate the spin-1/2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordstrom…
Space-time--time is a natural hybrid of Kaluza's five-dimensional geometry and Weyl's conformal space-time geometry. Translations along the secondary time dimension produce the electromagnetic gauge transformations of Kaluza--Klein theory…
A four-vector field in flat space-time, satisfying a gauge-invariant set of second-order differential equations, is considered as a unified field. The model variational principle corresponds to the general covariance idea and gives rise to…
The equations of motion for $N$ non-relativistic particles attracting according to Newton's law are shown to correspond to the equations for null geodesics in a $(3N+2)$-dimensional Lorentzian, Ricci-flat, spacetime with a covariantly…
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…
We discuss kinematical properties of a free relativistic particle with deformed phase space in which momentum space is given by (a submanifold of) de Sitter space. We provide a detailed derivation of the action, Hamiltonian structure and…
It is argued that a noncommutative geometry of spacetime leads to a reconciliation of electromagnetism and gravitation while providing an underpinning to Weyl's geometry. It also leads to a cosmology consistent with observation. A few other…
A review is made of recent efforts to define linear connections and their corresponding curvature within the context of noncommutative geometry. As an application it is suggested that it is possible to identify the gravitational field as a…
The classical dynamics and the construction of quantum states in a plane wave curved spacetime are examined, paying particular attention to the similarities with the case of an electromagnetic plane wave in flat spacetime. A natural map…
The Hamiltonian formulation with action-angle variables is very useful when considering the motion of particles undergoing a self-force reaction due to gravitational wave emission. Using the proper time as a parameter along the trajectory…
One of the deepest insights from the general theory of relativity is the relational nature of spacetime. While it is a generally agreed on that the nature of spacetime must be drastically different at the Planck scale, it has been a common…
The internal space-time symmetries of relativistic particles are dictated by Wigner's little groups. The $O(3)$-like little group for a massive particle at rest and the $E(2)$-like little group of a massless particle are two different…
This article devoted to relativistic dynamics of a charged massive particle in an electroscalar field. It represents a continuation of paper [1] where the authors constructed a non-relativistic theory which describes transverse…
A deformed relativistic kinematics can be understood within a geometrical framework through a maximally symmetric momentum space. However, when considering this kind of approach, usually one works in a flat spacetime and in a curved…