Related papers: Variational generalization of free relativistic to…
Problems involving rolling without slipping or no sideways skidding, to name a few, introduce velocity-dependent constraints that can be efficiently treated by the method of Lagrange multipliers in the Lagrangian formulation of the…
The conformal equivalence of fourth-order gravity following from a non-linear Lagrangian L(R) to theories of other types is widely known, here we report on a new conformal equivalence of these theories to theories of the same type but with…
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…
We consider the most general class of teleparallel theories of gravity quadratic in the torsion tensor, and carry out a detailed investigation of its Hamiltonian formulation in the time gauge. Such general class is given by a…
We consider a (2+1)-dimensional mechanical system with the Lagrangian linear in the torsion of a light-like curve. We give Hamiltonian formulation of this system and show that its mass and spin spectra are defined by one-dimensional…
We propose the Lagrangian formulation for describing the motion of a test particle in a general relativistic, stationary, and axially symmetric spacetime. The test particle is also affected by a radiation field, modeled as a coherent flux…
We present a Lagrangian formulation for 4d integer-spin relativistic fields in the 5d space spanned by two conjugate Weyl spinors and a Lorentz-invariant proper-time coordinate. We construct a manifestly Poincare-invariant free classical…
We formulate higher order variations of a Lagrangian in the geometric framework of jet prolongations of fibered manifolds. Our formalism applies to Lagrangians which depend on an arbitrary number of independent and dependent variables,…
We consider the motion of a point particle with spin in a stationary spacetime. We define, following Witzany (2019) and later Ramond (2022), a twelve dimensional Hamiltonian dynamical system whose orbits coincide with the solutions of the…
The Einstein initial-value equations in the extrinsic curvature (Hamiltonian) representation and conformal thin sandwich (Lagrangian) representation are brought into complete conformity by the use of a decomposition of symmetric tensors…
The evidence of the acceleration of universe at present time has lead to investigate modified theories of gravity and alternative theories of gravity, which are able to explain acceleration from a theoretical viewpoint without the need of…
A variational formulation for the geodesic circles in two-dimensional Riemannian manifold is discovered. Some relations with the uniform relativistic acceleration and the one-dimensional 'spin'-curvature interaction is investigated.
Relativistic particles with higher spin can be described in first quantization using actions with local supersymmetry on the worldline. First, we present a brief review of these actions and their use in first quantization. In a Dirac…
The minimal Hamiltonian for a family of relativistic rotators is constructed by a direct application of the Dirac procedure for constrained systems. The Hamiltonian equations can be easily solved. It is found that the resulting motion is…
The Lagrangian equations of motion for massive spinning test particles (tops) moving on a gravitational background using General Relativity are presented. The paths followed by tops are nongeodesic. An exact solution for the motion of tops…
In a foregoing paper, gravity has been interpreted as the pressure force exerted on matter at the scale of elementary particles by a perfect fluid. Under the condition that Newtonian gravity must be recovered in the incompressible case, a…
Modifications of General Relativity usually include extra dynamical degrees of freedom, which to date remain undetected. Here we explore the possibility of modifying Einstein's theory by adding solely nondynamical fields. With the minimal…
We propose a new world-line Lagrangian model of the D=4 massless relativistic particle with continuous spin and develop its twistorial formulation. The description uses two Penrose twistors subjected to four first class constraints. After…
We extend the results of our previous work on the conformal invariant description of two relativistic point particles. We consider here the most general lagrangian by using a conformal tensor $h_{\mu\nu}$, transforming as a Wilson line, and…
We show that Wigner's infinite spin particle classically is described by a reparametrization invariant higher order geometrical Lagrangian. The model exhibit unconventional features like tachyonic behaviour and momenta proportional to…