Related papers: Nonabelian fluids and helicities
In conventional gauge theory, a charged point particle is described by a representation of the gauge group. If we propagate the particle along some path, the parallel transport of the gauge connection acts on this representation. The…
We consider the Euler equations of incompressible inviscid fluid dynamics. We discuss a variational formulation of the governing equations in Lagrangian coordinates. We compute variational symmetries of the action functional and generate…
We consider a scalar field action for which the Lagrangian density is a power of the massless Klein-Gordon Lagrangian. The coupling of gravity to this matter action is considered. In this case, we show the existence of nontrivial scalar…
This article is a detailed version of our short letter `On equilibrium partition function for non-relativistic fluid' [arXiv:1505.05677] extended to include an anomalous $U(1)$ symmetry. We construct a relativistic system, which we call…
It is known that the dynamics of dissipative fluids in Eulerian variables can be derived from an algebra of Leibniz brackets of observables, the metriplectic algebra, that extends the Poisson algebra of the zero viscosity limit via a…
We develop further the formalism of the non-Abelian gauge field theory on a cell complex space-time and show how the gauge-invariant action and the equations of motion for gauge fields interacting with spinors can be written without a…
By a semi-Lagrangian change of coordinates, the hydrostatic Euler equations describing free-surface sheared flows is rewritten as a system of quasilinear equations, where stability conditions can be determined by the analysis of its…
A Lagrangian formulation of perfect fluid due to a noncanonical three-form field is investigated. The thermodynamic quantities such as energy density, pressure and the four velocity are obtained and then analyzed by comparing with the…
Given a fluid equation with reduced Lagrangian $l$ which is a functional of velocity $\MM{u}$ and advected density $D$ given in Eulerian coordinates, we give a general method for semidiscretising the equations to give a canonical…
A thermodynamic analysis of weakly nonlocal non-relativistic fluids is presented under the assumption that an additional scalar field also contributes to the dynamics. The most general evolution of this field and the constitutive relations…
We investigate certain invariance properties of quantum fluids subject to a nonlinear gauge potential. In particular, we derive the covariant transformation laws for the nonlinear potentials under a space-time Galilean boost and consider…
Some recently proposed approximations to follow the non--linear evolution of collisionless matter perturbations in the universe are reviewed. The first one, called frozen--flow approximation, is an Eulerian method within Newtonian theory,…
The Hamiltonian formulation for perfect fluid equations with the l-conformal Galilei symmetry is proposed. For an arbitrary half-integer value of the parameter l, the Hamilton and non-canonical Poisson brackets are found, in terms of which…
We discuss general properties and possible types of magnetic vortices in non-Abelian gauge theories (we consider here $G= SU(N), SO(N), USp(2N)$) in the Higgs phase. The sources of such vortices carry "fractional" quantum numbers such as…
Arnold pointed out that the Euler equation of incompressible ideal hydrodynamics describes geodesics on the group of volume-preserving diffeomorphisms. A simple analogue is the Euler equation for a rigid body, which is the geodesic equation…
We begin by placing the Generalized Lagrangian Mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincar\'e (EP) variational framework of fluid dynamics, for an averaged Lagrangian. We then derive a set of approximate…
After recalling the differential geometry of non-metric connections in the formalism of differential forms, we introduce the idea of a Non-Metricity (NM) connection, whose connection $1$--forms coincides with the non-metricity $1$--forms…
The Seiberg-Witten formalism has been realized as an electrodynamics in phase space (associated to the Dirac equation written in phase space) and this fact is explored here with non-abelian gauge group. First, a physically heuristic…
The symmetries of a free incompressible fluid span the Galilei group, augmented with independent dilations of space and time. When the fluid is compressible, the symmetry is enlarged to the expanded Schroedinger group, which also involves,…
Recent theoretical work has developed the Hamilton's-principle analog of Lie-Poisson Hamiltonian systems defined on semidirect products. The main theoretical results are twofold: (1) Euler-Poincar\'e equations (the Lagrangian analog of…