Non-Abelian fluid dynamics in Lagrangian formulation

Abstract

Non-Abelian extensions of fluid dynamics, which can have applications to the quark-gluon plasma, are given. These theories are presented in a symplectic/Lagrangian formulation and involve a fluid generalization of the Kirillov-Kostant form well known in Lie group theory. In our simplest model the fluid flows with velocity v and in presence of non-Abelian chromoelectric/magnetic E a /B a fields, the fluid feels a Lorentz force of the form QaE a + (v/c) × QaB a , where Qa is a space-time local non-Abelian charge satisfying a fluid Wong equation [(Dt + v · D)Q]a = 0 with gauge covariant derivatives.

Quaternionic Madelung transformation and non-Abelian fluid dynamics

“…These are a particularly natural set of equations for a non-abelian fluid, and differ from those obtained by Bistrovic et al only by a global gauge transformation [1]. Because we have obtained these equations by a transformation of the quaternionic Schroedinger equation, and because many techniques for simulating complex quantum mechanics generalize straightforwardly to the quaternionic case, our observation leads to simple algorithms for the computer simulation of non-abelian fluids.…”

“…Recently, there has been interest in developing non-abelian fluid dynamical models to describe systems such as quark-gluon plasmas, where one may wish the color degrees of freedom to be retained in the fluid description [1,3,4]. The color degrees of freedom are associated with the gauge symmetry group of the field; for the example of a quark-gluon plasma this would be the group SU(3) of quantum chromodynamics (QCD).…”

Perfect fluid theory and its extensions

“…At the same time, the analysis based on the kinetic equations still remains useful to us as a guide for arriving at the equations of interest. Our analysis is based on the paper in Ref [43].…”

A cyclic universe with colour fields

“…Then, the second boundary condition for a non-compact manifold will be One should also take into account torsion which, in the case of a 3-manifold, has three degrees of freedom [142][143][144][145][146], and which would lead to the nonlinear IvanenkoHeisenberg equation [147][148][149][150][151] and nonabelian degrees of freedom. The corresponding field would have a topological quantum number -the colour analogy of helicity in fluid dynamics [152][153][154]. In the three-dimensional case there are six possible helical flow orientations, as distinct from, for instance, two-dimensional flow, with its bipolar 54 Brought to you by | MIT Libraries Authenticated Download Date | 5/9/18 1:07 PM vorticity and only four possible flow orientations [155,156].…”