Related papers: (3+1)-dimensional compressible fluid as a (4+1)-di…
Explicit expressions of the 3D velocity field in terms of the conserved quantities of ideal fluid thermocline theory, namely Bernoulli function, density, and potential vorticity, are generalised here to a compressible ocean with a realistic…
3+1-dimensional free inviscid fluid dynamics is shown to satisfy the criteria for exact integrability, i.e. having an infinite set of independent, conserved quantities in involution, with the Hamiltonian being one of them. With (density…
The classical spin model in planar condensed media is represented as the U(1) Chern-Simons gauge field theory. When the vorticity of the continuous flow of the media coincides with the statistical magnetic field, which is necessary for the…
The Eulerian perfect-fluid theory is reformulated from its action principle in a pure field-theoretic manner. Conservation of the convective current is no longer imposed by Lin's constraints, but rather adopted as the central idea of the…
The motion of an incompressible fluid in Lagrangian coordinates involves infinitely many symmetries generated by the left Lie algebra of group of volume preserving diffeomorphisms of the three dimensional domain occupied by the fluid.…
The classical theory of non-relativistic charged particle interacting with U(1) gauge field is reformulated as the Schr\"odinger wave equation modified by the de-Broglie-Bohm quantum potential nonlinearity. For, (1 - $\hbar^2$) deformed…
A kinetic theory of classical particles serves as a unified basis for developing a geometric $3+1$ spacetime perspective on fluid dynamics capable of embracing both Minkowski and Galilei/Newton spacetimes. Parallel treatment of these cases…
Within the framework of the (3+1)-dimensional Lorentz-violating extended electrodynamics including the CPT-odd Chern-Simons term, we consider the electromagnetic field between the two parallel perfectly conducting plates. We find the…
The two-dimensional ideal (Euler) fluids can be described by the classical fields of streamfunction, velocity and vorticity and, in an equivalent manner, by a model of discrete point-like vortices interacting in plane by a self-generated…
We consider the 3D compressible isentropic Euler equations describing the motion of a liquid in an unbounded initial domain with a moving boundary and a fixed flat bottom at finite depth. The liquid is under the influence of gravity and…
Euler hydrodynamics of perfect fluids can be viewed as an effective bosonic field theory. In cases when the underlying microscopic system involves Dirac fermions, the quantum anomalies should be properly described. In 1+1 dimensions the…
We show that the incompressible Euler equations in three spatial dimensions can be expressed in terms of an abelian gauge theory with a topological BF term. A crucial part of the theory is a 3-form field strength, which is dual to a…
The Euler equation for an inviscid, incompressible fluid in a three-dimensional domain M implies that the vorticity is a frozen-in field. This can be used to construct a symplectic structure on RxM. The normalized vorticity and the…
The helicity is a topological conserved quantity of the Euler equations which imposes significant constraints on the dynamics of vortex lines. In the compressible setting the conservation law only holds under the assumption that the…
In this presentation we review our work on Abelian Maxwell-Chern-Simons theory in three-dimensional AdS black brane backgrounds, with both integer and non-integer Chern-Simons coupling. Such theories can be derived from several string…
We study the electrodynamics of generic charged particles (bosons, fermions, relativistic or not) constrained to move on an infinite plane. An effective gauge theory in 2+1 dimensional spacetime which describes the real electromagnetic…
The shallow water equations describe the horizontal flow of a thin layer of fluid with varying height. We show that the equations can be rewritten as a d=2+1 dimensional gauge theory with a Chern-Simons term. The theory contains two Abelian…
We introduce and investigate new models of the Chern-Simons type in the three-dimensional spacetime, focusing on the existence of compact vortices. The models are controlled by potentials driven by a single real parameter that can be used…
In (2+1) dimensions, the Maxwell term $-(1/4) F_{\alpha\beta}F^{\alpha\beta}$ can be replaced by the Chern-Simons three-form $(\kappa/4)\epsilon^{\alpha\beta\gamma}A_\alpha F_{\beta\gamma}$, yielding a novel type of `electromagnetism'. This…
On the basis of gauge principle in the field theory, a new variational formulation is presented for flows of an ideal fluid. The fluid is defined thermodynamically by mass density and entropy density, and its flow fields are characterized…