Chaos, Scaling and Existence of a Continuum Limit in Classical Non-Abelian Lattice Gauge Theory

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dc.creatorNielsen, Holger Bech
dc.creatorRugh, Hans Henrik
dc.creatorRugh, Svend Erik
dc.date1996-11-18
dc.date.accessioned2026-07-07T09:14:35Z
dc.date.available2026-07-07T09:14:35Z
dc.descriptionWe discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a ``no go'' for simulating the original continuum classical gauge fields over a long time span since there is a never ending dynamical cascading towards the ultraviolet. We note that the temporal chaotic properties of the original continuum gauge fields and the lattice gauge system have entirely different scaling properties thereby emphasizing that they are entirely different dynamical systems which have only very little in common. Considered as a statistical system in its own right the lattice gauge system in a situation where it has reached equilibrium comes closest to what could be termed a ``continuum limit'' in the limit of very small energies (weak non-linearities). We discuss the lattice system both in the limit for small energies and in the limit of high energies where we show that there is a saturation of the temporal chaos as a pure lattice artifact. Our discussion focuses not only on the temporal correlations but to a large extent also on the spatial correlations in the lattice system. We argue that various conclusions of physics have been based on monitoring the non-Abelian lattice system in regimes where the fields are correlated over few lattice units only. This is further evidenced by comparison with results for Abelian lattice gauge theory. How the real time simulations of the classical lattice gauge theory may reach contact with the real time evolution of (semi-classical aspects of) the quantum gauge theory (e.g. Q.C.D.) is left as an important question to be further examined.
dc.description10 pages, LaTeX, 1 Postscript figure, uses stwol.sty (included). Talk presented at the 28th Int. Conf. on H.E.P. in Warsaw
dc.identifierhttps://arxiv.org/abs/hep-th/9611128
dc.identifierhttp://arxiv.org/abs/hep-th/9611128
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152721
dc.subjectHigh Energy Physics - Theory
dc.subjectChaotic Dynamics
dc.subjectHigh Energy Physics - Lattice
dc.subjectHigh Energy Physics - Phenomenology
dc.titleChaos, Scaling and Existence of a Continuum Limit in Classical Non-Abelian Lattice Gauge Theory
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