Eur. Phys. J. C (2016) 76: 688
https://doi.org/10.1140/epjc/s10052-016-4523-9

Regular Article - Theoretical Physics

Time evolution of linearized gauge field fluctuations on a real-time lattice

¹ Theoretical Physics Department, CERN, Geneva, Switzerland
² Faculty of Science and Technology, University of Stavanger, 4036, Stavanger, Norway
³ Department of Physics, University of Jyväskylä, P.O. Box 35, 40014, Jyväskylä, Finland
⁴ Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, 00014, Helsinki, Finland

^* e-mail: jarkko.t.peuron@student.jyu.fi

Received: 7 October 2016
Accepted: 21 November 2016
Published online: 16 December 2016

Abstract

Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Due to instabilities, small quantum fluctuations on top of the classical background may significantly affect the dynamics of the system. In this paper we argue for the need for a numerical calculation of a system of classical gauge fields and small linearized fluctuations in a way that keeps the separation between the two manifest. We derive and test an explicit algorithm to solve these equations on the lattice, maintaining gauge invariance and Gauss’ law.