Quantization of space-time and the corresponding quantum mechanics |
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Authors: | M Banai |
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Institution: | (1) Central Research Institute for Physics, P.O.B. 49, H-1525 Budapest 114, Hungary |
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Abstract: | An axiomatic framework for describing general space-time models is presented. Space-time models to which irreducible propositional systems belong as causal logics are quantum (q) theoretically interpretable and their event spaces are Hilbert spaces. Such aq space-time is proposed via a canonical quantization. As a basic assumption, the time t and the radial coordinate r of aq particle satisfy the canonical commutation relation t,r]=±i
. The two cases will be considered simultaneously. In that case the event space is the Hilbert space L2( 3). Unitary symmetries consist of Poincaré-like symmetries (translations, rotations, and inversion) and of gauge-like symmetries. Space inversion implies time inversion. Thisq space-time reveals a confinement phenomenon: Theq particle is confined in an
size region of Minkowski space
at any time. One particle mechanics overq space-time provides mass eigenvalue equations for elementary particles. Prugove ki's stochasticq mechanics andq space-time offer a natural way for introducing and interpreting consistently such aq space-time andq particles existing in it. The mass eigenstates ofq particles generate Prugove ki's extended elementary particles. When
0, these particles shrink to point particles and
is recovered as the classical (c) limit ofq space-time. Conceptual considerations favor the case t,r]=+i
, and applications in hadron physics give the fit
2/5 fermi/GeV.This paper is a revised version of the author's work, Quantization of Space-time and the Corresponding Quantum Mechanics (Part I), report KFKI-1981-48. |
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Keywords: | |
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