Stochastic localization, quantum mechanics on phase space and quantum space-time

1985 ◽  
Vol 8 (11) ◽  
pp. 1-128 ◽  
Author(s):  
S. Twareque Ali
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Space Time ◽  
Quantum Space

scholarly journals A Quantum Space behind Simple Quantum Mechanics

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Chuan Sheng Chew ◽  
Otto C. W. Kong ◽  
Jason Payne
Keyword(s):  
Quantum Mechanics ◽  
Theoretical Model ◽  
Phase Space ◽  
Configuration Space ◽  
Center Of Mass ◽  
Free Particle ◽  
Physical Space ◽  
Dimensional Manifold ◽  
Quantum Space ◽  
Simple Quantum

In physics, experiments ultimately inform us about what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the configuration space of a free particle (or the center of mass of a closed system of particles). This configuration space (as well as phase space) can be constructed as a representation space for the relativity symmetry. From the corresponding quantum symmetry, we illustrate the construction of a quantum configuration space, similar to that of quantum phase space, and recover the classical picture as an approximation through a contraction of the (relativity) symmetry and its representations. The quantum Hilbert space reduces into a sum of one-dimensional representations for the observable algebra, with the only admissible states given by coherent states and position eigenstates for the phase and configuration space pictures, respectively. This analysis, founded firmly on known physics, provides a quantum picture of physical space beyond that of a finite-dimensional manifold and provides a crucial first link for any theoretical model of quantum space-time at levels beyond simple quantum mechanics. It also suggests looking at quantum physics from a different perspective.

Сonanical quantum space-time and the arrow time

2020 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Space Time ◽  
Quantum Space

Сonanical quantum space-time and the arrow time

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 Quantum space–time and classical gravity

1998 ◽  
Vol 39 (1) ◽  
pp. 423-442 ◽  
Author(s):  
J. Madore ◽  
J. Mourad
Keyword(s):  
Space Time ◽  
Quantum Space ◽  
Classical Gravity

Formulation of Quantum Mechanics Based on the Quasi-Probability Distribution Induced on Phase Space

1958 ◽  
Vol 109 (6) ◽  
pp. 2198-2206 ◽  
Author(s):  
George A. Baker
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Probability Distribution

Quantum Space-Time Groups and Beyond

1997 ◽  
pp. 297-312
Author(s):  
Mariano A. del Olmo
Keyword(s):  
Space Time ◽  
Quantum Space

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 A geometric renormalization group in discrete quantum space–time

2003 ◽  
Vol 44 (12) ◽  
pp. 5588 ◽  
Author(s):  
Manfred Requardt
Keyword(s):  
Renormalization Group ◽  
Space Time ◽  
Quantum Space
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