Chaos, Scaling and Existence of a Continuum Limit in Classical NonAbelian Lattice Gauge Theory
Abstract
We discuss spacetime chaos and scaling properties for classical nonAbelian 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 nonlinearities). 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 nonAbelian 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 (semiclassical aspects of) the quantum gauge theory (e.g. Q.C.D.) is left as an important question to be further examined.
 Publication:

arXiv eprints
 Pub Date:
 November 1996
 DOI:
 10.48550/arXiv.hepth/9611128
 arXiv:
 arXiv:hepth/9611128
 Bibcode:
 1996hep.th...11128N
 Keywords:

 High Energy Physics  Theory;
 High Energy Physics  Lattice;
 High Energy Physics  Phenomenology;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 10 pages, LaTeX, 1 Postscript figure, uses stwol.sty (included). Talk presented at the 28th Int. Conf. on H.E.P. in Warsaw