Related papers: A 4-vector formalism for classical mechanics

On the basis of dynamic quantization method we build in this paper a new mathematically correct quantization scheme of gravity. In the frame of this scheme we develop a canonical formalism in tetrad-connection variables in 4-D theory of…

One of the key ways in which quantum mechanics differs from relativity is that it requires a fixed background reference frame for spacetime. In fact, this appears to be one of the main conceptual obstacles to uniting the two theories.…

We take causality and uniqueness of events observation as our driving forces. They are built in in the way we define distinct observers, which then require a finite time to communicate between each other. This unavoidably leads to the…

We present a comprehensive introduction to the kinematics of special relativity based on Minkowski diagrams and provide a graphical alternative to each and every topic covered in a standard introductory sequence. Compared to existing…

The class of relativistic spin particle models reveals the `quantization' of parameters already at the classical level. The special parameter values emerge if one requires the maximality of classical global continuous symmetries. The same…

Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…

In this paper we present definitions of different four-dimensional (4D) geometric quantities (Clifford multivectors). New decompositions of the torque N and the angular momentum M (bivectors) into 1-vectors N_{s}, N_{t} and M_{s}, M_{t}…

The phenomenology of quantum systems in curved space-times is among the most fascinating fields of physics, allowing --often at the gedankenexperiment level-- constraints on tentative theories of quantum gravity. Determining the dynamics of…

Category theory plays a special character in mathematics - it unifies distinct branches under the same formalism. Despite this integrative power in math, it also seems to provide the proper foundations to the experimental physicist. In this…

This article shows how to express relativistic concepts in a visual manner using the full power of hyperbolic trigonometric functions. Minkowski diagrams in energy-momentum space are used in conjunction with hyperbolic triangles. Elegant…

It is shown that application of dynamic flows concept in 4-dimensional Euclidean space makes possible to form Minkowski space and to formulate the generalized variational problem of electrodynamics and gravi- dynamics. It is shown that…

The expansion of a classical Hamilton formalism consisting in adaptation of it to describe the nonequilibrium systems is offered. Expansion is obtained by construction of formalism on the basis of the dynamics equation of the equilibrium…

Motion of a classical particle in 3-dimensional Lobachevsky and Riemann spaces is studied in the presence of an external magnetic field which is analogous to a constant uniform magnetic field in Euclidean space. In both cases three…

We present a formalism for light optics starting with the Maxwell equations and casting them into an exact matrix form taking into account the spatial and temporal variations of the permittivity and permeability. This $8 \times 8$ matrix…

After a review of the problems induced by the Lorentz signature of Minkowski space-time, like the need of a clock synchronization convention for the definition of 3-space and the complexity of the notion of relativistic center of mass,…

In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of…

After a review of the canonical reduction to the rest-frame Wigner-covariant instant form of standard theories in Minkowski spacetime, a new formulation of tetrad gravity is introduced. Its canonical reduction, also in presence of N scalar…

We give a unitary irreducible representation of the proper Poincar\'e group that leads to an operational version of the classical relativistic dynamics of a massive spinless particle. Unlike quantum mechanics, in this operational theory…

I present a covariant approach to developing 1+3 formalism without an introduction of any basis or coordinates. In the formalism, a spacetime which has a timelike congruence is assumed. Then, tensors are split into temporal and spatial…

It is widely believed that classical gravity breaks down and quantum gravity is needed to deal with a singularity. We show that there is a class of spacetime curvature singularities which can be resolved with metric and matter field…