Related papers: Relativistic generalization of the Schrodinger-New…
We consider the asymptotic behaviour of small-amplitude gravity water waves in a rectangular domain where the water depth is much smaller than the horizontal scale. The control acts on one lateral boundary, by imposing the horizontal…
We show that the Schr\"odinger equation can be derived assuming the Galilean covariance of a generic wave equation and the validity of the de Broglie's wave-particle duality hypothesis. We also obtain from this set of assumptions the…
In \cite{2} it was shown that Einstein's special theory of relativity and Maxwell's field theory have mathematically equivalent dual versions. The dual versions arise from an identity relating observer time to proper time as a contact…
We show how the Dirac equation in three space-dimensions emerges from the large-scale dynamics of the minimal nontrivial quantum cellular automaton satisfying unitariety, locality, homogeneity, and discrete isotropy, without using the…
The wave Schrodinger and, to clarify one interesting point encountered in the calculations, Klein-Gordon equations are solved exactly for a single neutron moving in a central Woods-Saxon plus an additional potential that provides a…
Newton's second law may be used to obtain a wave equation, which reduces to Schrodinger's equation in the nonrelativistic limit and for a conservative force.
In this article we present a particular theory of gravity in which Einstein's field equations are modified by promoting Newton's constant $G$ to a covariant differential operator $G_\Lambda(\Box_g)$. The general idea was obviously outlined…
We examine the weak-field approximation of locally Galilean invariant gravitational theories with general covariance in a $(4+1)$-dimensional Galilean framework. The additional degrees of freedom allow us to obtain Poisson, diffusion, and…
It is shown that a recently proposed model for the gravitational interaction in non relativistic quantum mechanics is the instantaneous action at a distance limit of a field theoretic model containing a negative energy field. It reduces to…
We find vacuum solutions such that massive gravitons are confined in a local spacetime region by their gravitational energy in asymptotically flat spacetimes in the context of the bigravity theory. We call such self-gravitating objects…
In the present work we propose a generalization of Newton's gravitational theory from the original works of Heaviside and Sciama, that takes into account both approaches, and accomplishes the same result in a simpler way than the standard…
The analysis of a general multibody physical system governed by Einstein's equations in quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties -- many coupled degrees of freedom, dynamic instability --…
We present a new approximation to include fully general relativistic pressure and velocity in Newtonian hydrodynamics. The energy conservation, momentum conservation and two Poisson's equations are consistently derived from Einstein's…
The intrinsic metric symmetries for energy-momentum in warped space-time universally reinforce strict spatial flatness in the GR metric formalism. The passive/active energy-charge for the 1686, 1913, and 1915 gravitational laws maintains…
We present the generalization of a recently introduced modified gravitational potential for self-gravitating fluids. The use of this potential allows for an accurate approximation of general relativistic effects in an otherwise Newtonian…
Ultracold neutrons are great experimental tools to explore the gravitational interaction in the regime of quantized states. From a theoretical perspective, starting from a Dirac equation in curved spacetime, we applied a perturbative scheme…
This is the more technical half of a two-part work in which we introduce a robust microlocal framework for analyzing the non-relativistic limit of relativistic wave equations with time-dependent coefficients, focusing on the Klein--Gordon…
We apply the principles discussed in an earlier paper to the construction of discrete time field theories. We derive the discrete time field equations of motion and Noether's theorem and apply them to the Schrodinger equation to illustrate…
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear…
In the weak-field limit of General Relativity, gravitational waves obey linear equations and propagate at the speed of light. These properties of General Relativity are supported by the observation of ultra high energy cosmic rays as well…