Chaos, scaling and existence of a continuum limit in classical non-Abelian lattice gauge theory

Conference · Tue Dec 31 04:00:00 EST 1996

OSTI ID:442155

Nielsen, H B ^[1]; Rugh, H H ^[2]; Rugh, S E ^[3]

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1. Niels Bohr Inst., Kobenhavn (Denmark)
2. Univ. of Warwick, Coventry (United Kingdom)
3. Los Alamos National Lab., NM (United States)

We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a {open_quote}no go{close_quotes} 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 {open_quotes}continuum limit{close_quotes} 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 an important question to be further examined.

• Research Organization: Los Alamos National Lab., NM (United States)
• Sponsoring Organization: USDOE Assistant Secretary for Human Resources and Administration, Washington, DC (United States); National Science Foundation, Washington, DC (United States); California Univ., Berkeley, CA (United States)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 442155
• Report Number(s): LA-UR--96-4455; CONF-960765--51; ON: DE97003136; CNN: Grant PHY94-07194
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
HAMILTONIANS
LATTICE FIELD THEORY
RANDOMNESS
SPACE-TIME