Related papers: Third post-Newtonian constrained canonical dynamic…
A pure Dirac's framework for 3D Palatini's theory with cosmological constant is performed. By considering the complete phase space, we find out the full structure of the constraints, and their corresponding algebra is computed explicitly.…
Recently proposed new gauge invariant formulation of the Chern-Simons gauge theory is considered in detail. This formulation is consistent with the gauge fixed formulation. Furthermore it is found that the canonical (Noether) Poincar\'e…
General relativity has been very successful since its proposal more a century ago. However, various cosmological observations and theoretical consistency still motivate us to explore extended gravity theories. Horndeski gravity stands out…
We address the post-collapse dynamics of a self-gravitating gas of Brownian particles in D dimensions, in both canonical and microcanonical ensembles. In the canonical ensemble, the post-collapse evolution is marked by the formation of a…
We consider a relativistic extended object described by a reparametrization invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the…
We parameterize the second post-Newtonian (2PN) metric for a gravitating system of fluids in the generalized harmonic gauge, and find that there are only three independent 2PN parameters (i.e. $\omega$, $\delta$ and $\delta_2$) for…
We apply the Dirac procedure for constrained systems to the Arnowitt-Deser-Misner formalism linearized around the Friedmann-Lemaitre universe. We explain and employ some basic concepts such as Dirac observables, Dirac brackets, gauge-fixing…
Two Fokker actions and corresponding equations of motion are obtained for two point particles in a post-Minkowski framework, in which the field of each particle is given by the half-retarded + half-advanced solution to the linearized…
We report on recent results obtained in the post-Newtonian framework for the modelling of the gravitational waves emitted by binary systems of spinning compact objects (black holes and/or neutron stars). These new results are obtained at…
In this article, we introduce and develop the notion of parametrised Poincar\'{e} duality in the formalism of parametrised higher category theory by Martini-Wolf, in part generalising Cnossen's theory of twisted ambidexterity to the…
We consider the two-body problem in post-Newtonian approximations of general relativity. We report the recent results concerning the equations of motion, and the associated Lagrangian formulation, of compact binary systems, at the third…
The Hamilton theories for higher orders classical Lagrange functions result on a well known Ostrogradski's instabilities. In this work, we propose a different definition for the second order canonical momentum and obtain a new set of second…
When Einstein formulated his special relativity, he developed his dynamics for point particles. Of course, many valiant efforts have been made to extend his relativity to rigid bodies, but this subject is forgotten in history. This is…
We develop a Hamiltonian formalism suitable to be applied to gauge theories in the presence of Gravitation, and to Gravity itself when considered as a gauge theory. It is based on a nonlinear realization of the Poincar\'e group, taken as…
The Poincare mass operator can be represented in terms of a Cl(3,0) Clifford algebra. With this representation the quadratic Dirac equation and the Maxwell equations can be derived from the same mathematical structure.
We study the dynamics of N charges interacting with the Maxwell field. If their initial velocities are small compared to the velocity of light, c, then in lowest order their motion is governed by the static Coulomb Lagrangian. We…
The motion of compact binaries is influenced by the spin of their components starting at the 1.5 post-Newtonian (PN) order. On the other hand, in the large mass ratio limit, the spin of the lighter object appears in the equations of motion…
We study the coupling of N charged scalar particles plus the electro-magnetic field to ADM tetrad gravity and its canonical formulation in asymptotically Minkowskian space-times without super-translations. We make the canonical…
Starting from the coadjoint Poincar\'e algebra we construct a point particle relativistic model with an interpretation in terms of extra-dimensional variables. The starting coadjoint Poincar\'e algebra is able to induce a mechanism of…
We derive the path integral action for a particle moving in three dimensional fuzzy space. From this we extract the classical equations of motion. These equations have rather surprising and unconventional features: They predict a cut-off in…