Related papers: A 4-vector formalism for classical mechanics
A new framework for deriving equations of motion for constrained quantum systems is introduced, and a procedure for its implementation is outlined. In special cases the framework reduces to a quantum analogue of the Dirac theory of…
We describe an efficient scheme for evaluating higher order contributions to primordial cosmological perturbations using the "in-in" formalism, which is the basis of modern calculations of non-Gaussian and higher order contributions to the…
The rosette-shaped motion of a particle in a central force field is known to be classically solvable by quadratures. We present a new approach of describing and characterizing such motion based on the eccentricity vector of the two body…
A new systematic approach extending the notion of frames to the Palatini scalar-tensor theories of gravity in various dimensions n>2 is proposed. We impose frame transformation induced by the group action which includes almost-geodesic and…
Thermal scalar radiation in two spacetime dimensions is treated within relativistic classical physics. Part I involves an inertial frame where are given the analogues both of Boltzmann's derivation of the Stefan-Boltzmann law and also…
Minkowski space serves as a framework for the theoretical constructions that deal with manifestations of relativistic effects in physical phenomena. But neither Minkowski himself nor the subsequent developers of the relativity theory have…
As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…
The Minkowski's theory is regarded as the classical approach for describing the electromagnetism of uniformly moving objects by elegantly utilizing the format-invariance of the Maxwell's equations in inertia reference frames under Lorentz…
A relativistic classical field theory with zero-point radiation involves a vacuum corresponding to a scale-invariant spectrum of random classical radiation in spacetime with the overall constant chosen to give an energy (1/2)\hbar\omega per…
MOG as a modified gravity theory is designed to be replaced with dark matter. In this theory, in addition to the metric tensor, a massive vector is a gravity field where each particle has a charge proportional to the inertial mass and…
Starting from a simple classical framework and employing some stochastic concepts, the basic ingredients of the quantum formalism are recovered. It has been shown that the traditional axiomatic structure of quantum mechanics can be rebuilt,…
This work consists in the theorical development on the analysis of the Thermodynamic Laws and thermodynamic systems in relative motion, according to the laws of Classical Mechanics. The difference of this work for many of the literature is…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
A new scheme for numerical integration of motion for classical systems composed of rigid polyatomic molecules is proposed. The scheme is based on a matrix representation of the rotational degrees of freedom. The equations of motion are…
The Riemann -- Silberstein -- Majorana -- Oppengeimer approach to the Maxwell electrodynamics in presence of electrical sources and arbitrary media is investigated within the matrix formalism. The symmetry of the matrix Maxwell equation…
In this paper the analogues of the Lorentz transformations for non-inertial reference frames have been obtained. A common case when the movement speed of one coordinate frame in relation to another one can have time derivatives of higher…
Extra dimensions can be utilized to simplify problems in classical mechanics, offering new insights. Here we show a simple example of how the motion of a test particle under the influence of an inverse-quadratic potential in 1D is…
The complete explicitly covariant 4-dimensional description of the dynamics of a free classical particle with spin within the framework of the special relativity theory is presented. The key point of our approach is the the introduction of…
We give a brief summary of the formalism of invariants in general scalar-tensor and multiscalar-tensor gravities without derivative couplings. By rescaling of the metric and reparametrization of the scalar fields, the theory can be…
This paper is a serious attempt at reconciling quantum and classical mechanics through the concept of dynamic space and the acceptance of non-zero Ricci tensor for vacuum. Starting with scalar particles, the paper shows that with those two…