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arXiv:quant-ph/0604055

About mathematical apparatus of many body quantum dynamics

Yu. I. Ozhigov

Published Apr 8, 2006• 1 citation
arXivHTMLPDF

Abstract

We discuss the possibility to modify many-body Hilbert quantum formalism that is necessary for the representation of quantum systems dynamics. The notion of effective classical algorithm and visualization of quantum dynamics play the key role.
DOI
10.48550/arxiv.quant-ph/0604055

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A draft of a possible comparison between the use made of mathematics in classical field theories and in quantum mechanics is presented. Hilbert’s space formalism, although not only elegant and powerful but intuitive as well, does not give us a spatio-temporal representation of physical events. The picture of the electromagnetic field as an entity which is real in itself – i.e., as a wave without support – fostered by the emergence of special relativity can be seen as the first step, favored by many physicists and philosophers, of a gradual “escape” from intuition into a purely mathematical representation of the external world. After the introduction, in recent theoretical physics, of fiber bundle formalism the classical notion of field acquires a new spatio-temporal intuitiveness. This intuitiveness is clearly foreshadowed in the Kantian and Meinongian analysis of the notion of magnitude. At the end of the paper we show that, contrary to what happens in quantum mechanics, mathematics plays a truly explicative role in general relativity, without any loss of spatio-temporal intuitiveness.
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