On the Space-Time and State-Space Geometries of Random Processes in Geometric Quantum Mechanics

2007 ◽  
Author(s):  
Diego L. Rapoport
Keyword(s):  
Quantum Mechanics ◽  
State Space ◽  
Random Processes ◽  
Space Time ◽  
Geometric Quantum Mechanics

scholarly journals PROBABILITY IN RELATIVISTIC QUANTUM MECHANICS AND FOLIATION OF SPACE–TIME

2007 ◽  
Vol 22 (32) ◽  
pp. 6243-6251 ◽  
Author(s):  
HRVOJE NIKOLIĆ
Keyword(s):  
Quantum Mechanics ◽  
Wave Equations ◽  
Integral Curve ◽  
Relativistic Quantum ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Relativistic Wave ◽  
Probability Densities ◽  
The Many ◽  
Conserved Currents

The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be nonnegative and the integral of them over an entire hypersurface should be equal to one. To satisfy these requirements in a covariant manner, the foliation of space–time must be such that each integral curve of the current crosses each hypersurface of the foliation once and only once. In some cases, it is necessary to use hypersurfaces that are not spacelike everywhere. The generalization to the many-particle case is also possible.

scholarly journals Space time geometry in the atomic hydrogenoid system. Approach to a dust relativistic model from causal quantum mechanics

2018 ◽  
Vol 64 (1) ◽  
pp. 18
Author(s):  
G. Gómez ◽  
I. Kotsireas ◽  
I. Gkigkitzis ◽  
I. Haranas ◽  
M.J. Fullana
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
General Equation ◽  
System Approach ◽  
Space Time ◽  
Relativistic Model ◽  
Time Deformation ◽  
Non Local ◽  
De Broglie Bohm

Weintend to use the description oftheelectron orbital trajectory in the de Broglie-Bohm (dBB) theory to assimilate to a geodesiccorresponding to the General Relativity (GR) and get from itphysicalconclusions. ThedBBapproachindicatesustheexistenceof a non-local quantumfield (correspondingwiththequantumpotential), anelectromagneticfield and a comparativelyveryweakgravitatoryfield, togetherwith a translationkineticenergyofelectron. Ifweadmitthatthosefields and kineticenergy can deformthespace time, according to Einstein'sfield equations (and to avoidtheviolationoftheequivalenceprinciple as well), we can madethehypothesisthatthegeodesicsof this space-time deformation coincide withtheorbitsbelonging to thedBBapproach (hypothesisthat is coherentwiththestabilityofmatter). Fromit, we deduce a general equation that relates thecomponentsofthemetric tensor. Thenwe find anappropriatemetric for it, bymodificationofanexactsolutionofEinstein'sfield equations, whichcorresponds to dust in cylindricalsymmetry. Thefoundmodelproofs to be in agreementwiththebasicphysicalfeaturesofthehydrogenquantum system, particularlywiththeindependenceoftheelectronkineticmomentum in relationwiththeorbit radius. Moreover, themodel can be done Minkowski-like for a macroscopicshortdistancewith a convenientelectionof a constant. According to this approach, theguiding function ofthewaveontheparticlecould be identifiedwiththedeformationsofthespace-time and thestabilityofmatterwould be easilyjustifiedbythe null accelerationcorresponding to a geodesicorbit.

scholarly journals Supreme Theory of Everything

2019 ◽  
Vol 2 (2) ◽  
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Electromagnetic Wave ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Wave Particle Duality ◽  
Theory Of Everything ◽  
Parallel Universes ◽  
Celestial Bodies ◽  
Geometric Quantum Mechanics

Not only universe, but everything has general characters as eternal, infinite, cyclic and wave-particle duality. Everything from elementary particles to celestial bodies, from electromagnetic wave to gravity is in eternal motions, which dissects only to circle. Since everything is described only by trigonometry. Without trigonometry and mathematical circle, the science cannot indicate all the beauty of harmonic universe. Other method may be very good, but it is not perfect. Some part is very nice, another part is problematic. General Theory of Relativity holds that gravity is geometric. Quantum Mechanics describes all particles by wave function of trigonometry. In this paper using trigonometry, particularly mathematics circle, a possible version of the unification of partial theories, evolution history and structure of expanding universe, and the parallel universes are shown.

Remarks on geometric quantum mechanics

2004 ◽  
Vol 51 (2) ◽  
pp. 229-243 ◽  
Author(s):  
Alberto Benvegnù ◽  
Nicola Sansonetto ◽  
Mauro Spera
Keyword(s):  
Quantum Mechanics ◽  
Geometric Quantum Mechanics

scholarly journals Lp-valued stochastic convolution integral driven by Volterra noise

2018 ◽  
Vol 18 (06) ◽  
pp. 1850048 ◽  
Author(s):  
Petr Čoupek ◽  
Bohdan Maslowski ◽  
Martin Ondreját
Keyword(s):  
Banach Space ◽  
State Space ◽  
Stochastic Partial Differential Equations ◽  
Main Tool ◽  
Space Time ◽  
Convolution Integral ◽  
Hölder Continuous ◽  
Stochastic Convolution ◽  
Wiener Chaos ◽  
Convolution Integrals

Space-time regularity of linear stochastic partial differential equations is studied. The solution is defined in the mild sense in the state space [Formula: see text]. The corresponding regularity is obtained by showing that the stochastic convolution integrals are Hölder continuous in a suitable function space. In particular cases, this allows us to show space-time Hölder continuity of the solution. The main tool used is a hypercontractivity result on Banach-space valued random variables in a finite Wiener chaos.

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