5 research outputs found
"Gauging" the Fluid
A consistent framework has been put forward to quantize the isentropic,
compressible and inviscid fluid model in the Hamiltonian framework, using the
Clebsch parameterization. The naive quantization is hampered by the
non-canonical (in particular field dependent) Poisson Bracket algebra. To
overcome this problem, the Batalin-Tyutin \cite{12} quantization formalism is
adopted in which the original system is converted to a local gauge theory and
is embedded in a {\it canonical} extended phase space. In a different reduced
phase space scheme \cite{vy} also the original model is converted to a gauge
theory and subsequently the two distinct gauge invariant formulations of the
fluid model are related explicitly. This strengthens the equivalence between
the relativistic membrane (where a gauge invariance is manifest) and the fluid
(where the gauge symmetry is hidden). Relativistic generalizations of the
extended model is also touched upon.Comment: Version to appear in J.Phys. A: Mathematical and Genera
Perfect Fluid Theory and its Extensions
We review the canonical theory for perfect fluids, in Eulerian and Lagrangian
formulations. The theory is related to a description of extended structures in
higher dimensions. Internal symmetry and supersymmetry degrees of freedom are
incorporated. Additional miscellaneous subjects that are covered include
physical topics concerning quantization, as well as mathematical issues of
volume preserving diffeomorphisms and representations of Chern-Simons terms (=
vortex or magnetic helicity).Comment: 3 figure