相关论文: A variational formulation for relativistic mechani…

This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the…

The first part of this article develops a variational formulation for relativistic mechanics. The results are established through standard tools of variational analysis and differential geometry. The novelty here is that the main motion…

Witten's non-relativistic formalism of supersymmetric quantum mechanics was based on a factorization and partnership between Schroedinger equations. We show how it accommodates a transition to the partnership between relativistic…

We propose a form for the action of a relativistic particle subject to a positional force that is invariant under time reparametrization and therefore allows for a consistent Hamiltonian formulation of the dynamics. This approach can be…

Conventional relativistic quantum mechanics, based on the Klein-Gordon equation, does not possess a natural probabilistic interpretation in configuration space. The Bohmian interpretation, in which probabilities play a secondary role,…

We construct a relativistic quantum mechanics for a boson. To do this we exploit two component wave functions in Dirac type equations of motion. In our formalism we fix the pathological aspect of particle probability density which appears…

The logical inference approach to quantum theory, proposed earlier [Ann. Phys. 347 (2014) 45-73], is considered in a relativistic setting. It is shown that the Klein-Gordon equation for a massive, charged, and spinless particle derives from…

The relativistic Lagrangian in presence of potentials was formulated directly from the metric, with the classical Lagrangian shown embedded within it. Using it we formulated covariant equations of motion, a deformed Euler-Lagrange equation,…

The Schr\"odinger-type formalism of the Klein-Gordon quantum mechanics is adapted for the case of the $SL(2,\R)$ spacetime. The free particle case is solved, the results of a recent work are reproduced while all the other, topologically…

This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…

Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…

The formulation of a rigid body in relativistic quantum mechanics is studied. Departing from an alternate approach at the relativistic classical level, the corresponding Klein-Gordon and Dirac operators for the rigid body are obtained in…

We formulate quantum group Riemannian geometry as a gauge theory of quantum differential forms. We first develop (and slightly generalise) classical Riemannian geometry in a self-dual manner as a principal bundle frame resolution and a dual…

We develop an unified algebraic approach to the description of gauge interactions within the framework of a new concept of quantum mechanics. The next step in generalizing the space-time and the action vector space is made. The gauge field…

Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…

Lagrangian formulation of quantum mechanical Schr\"odinger equation is developed in general and illustrated in the eigenbasis of the Hamiltonian and in the coordinate representation. The Lagrangian formulation of physically plausible…

The causal stochastic interpretation of relativistic quantum mechanics has the problems of superluminal velocities, motion backward in time and the incorrect non-relativistic limit. In this paper, according to the original ideas of de…

A method of calculation for the variational derivatives for gravitational actions in the pseudo-Riemannian case is proposed as a practical variant of the first order formalism with constraints. The method is then used to derive the metric…

Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…

Relativistic mechanics on an arbitrary manifold is formulated in the terms of jets of its one-dimensional submanifolds. A generic relativistic Lagrangian is constructed. Relativistic mechanics on a pseudo-Riemannian manifold is particularly…