Related papers: On the geometrical hypotheses underlying wave func…
A previous derivation of the single-particle Schr\"odinger equation from statistical assumptions is generalized to an arbitrary number $N$ of particles moving in three-dimensional space. Spin and gauge fields are also taken into account. It…
Based on the Bohr's correspondence principle it is shown that relativistic mechanics and quantum mechanics may be considered as generalizations of classical mechanics. A comparative description of relativistic and classical mechanics is…
Mechanics is developed over a differentiable manifold as space of possible positions. Time is considered to fill a one--dimensional Riemannian manifold, so having the metric as lapse. Then the system is quantized with covariant instead of…
A derivation is presented of the quantummechanical wave equations based upon the Equity Principle of Einstein's General Relativity Theory. This is believed to be more generic than the common derivations based upon Einstein's energy…
A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…
It was recently shown that Newtonian dynamics of macroscopic particles can be derived from unitary Schr\"odinger evolution under an assumption on the system-environment interaction, namely that the interaction Hamiltonian effectively…
This paper explores the application of Newton-Cartan geometry to the kinetic theory of gases that includes non-relativistic gravitational effects and the principle of general covariance. Starting with an introduction to the basics of…
Using concepts of geometric orthogonality and linear independence, we logically deduce the form of the Pauli spin matrices and the relationships between the three spatially orthogonal basis sets of the spin-1/2 system. Rather than a…
The indeterministic character of physical laws is generally considered to be the most important consequence of quantum physics. A deterministic point of view, however, together with the possibility of well defined Hamiltonian trajectories,…
By quantising the gravitational dynamics, space and time are usually forced to play fundamentally different roles. This raises the question whether physically relevent configurations could also exist which would not admit…
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…
In textbooks on statistical mechanics, one finds often arguments based on classical mechanics, phase space and ergodicity in order to justify the second law of thermodynamics. However, the basic equations of motion of classical mechanics…
We introduce a geometrical framework to construct a large class of time-dependent quantum systems, in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over…
We do not know the symmetries underlying string theory. Furthermore, there must exist an inherently quantum, and spacetime independent, formulation of this theory. Independent of string theory, there should exist a description of quantum…
Dynamics of the structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The expression…
Aiming at providing an objective motion picture for the microscopic object described by the wave function, new analysis about motion is presented by use of the point set theory in mathematics, through which we show that a new kind of motion…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
We present a geometrical inspired study of the dynamics of $Dp$-branes. We focus on the usual nonpolynomial Dirac-Born-Infeld action for the worldvolume swept out by the brane in its evolution in general background spacetimes. We emphasize…
A new formulation of relativistic quantum mechanics is proposed in the framework of the rest-frame instant form of dynamics with its instantaneous Wigner 3-spaces and with its description of the particle world-lines by means of derived…
The main fundamental principles characterizing the vacuum field structure are formulated, the modeling of the related vacuum medium and charged point particle dynamics by means of devised field theoretic tools are analyzed. The Maxwell…