Metafluid dynamics as a gauge field theory

Abstract

In this paper, the analog of Maxwell electromagnetism for hydrodynamic turbulence, the metafluid dynamics, is extended in order to reformulate the metafluid dynamics as a gauge field theory. That analogy opens up the possibility to investigate this theory as a constrained system. Having this possibility in mind, we propose a Lagrangian to describe this new theory of turbulence and, subsequently, analyze it from the symplectic point of view. From this analysis, a hidden gauge symmetry is revealed, providing a clear interpretation and meaning of the physics behind the metafluid theory. Also, the geometrical interpretation to the gauge symmetries is discussed.

Metafluid dynamics and Hamilton-Jacobi formalism

“…In [9] the authors considered the case when sources are not zero. The interaction Lagrangian density L int = J. u − nφ − v u.∇n (18) was added to (17) and the total Lagrangian density corresponding to the metafluid dynamics can be written as…”

“…Using the Faddeev-Jackiw analysis [21] the set of constraints corresponding to (19) was obtained [9] as π 0 = 0, ∇. π + n = 0.…”

About Metafluid Dynamics

“…The metafluid dynamics was investigated from the symplectic point of view in [8] and using the projector method [14] a geometrical interpretation to the gauge symmetry of this theory was obtained.…”

“…On the other hand, the matrix M ij is projective and the infinitesimal gauge transformation is calculated as [8] …”

“…Another problem encountered in dealing with fractional Lagrangians densities, e.g. (8), is that the notion of the equivalent Lagrangians is not well-defined inside of the fractional calculus. In order to fulfill the above requirements we have to choose for our problem the Lagrangian density to start with as follows…”