Quantization and fluid mechanics?

[quantumfireball]

Quantization and fluid mechanics??

Cant quantum field theory be applied to releativistic imcompressible fluids?
cant the velocity vector field be quantized?
will the pressure of the fluid play the role of the 4th component of the four vector?
what would be the corresponding quanta?
(I know this might sound extremely stupid
but ......)

 

[jostpuur]

I don't know about this, but I must ask that is there Lagrangian formulation available for the Navier-Stokes system? If there is, then it could be possible to proceed with somewhat similar techniques as with the other quantum fields too.

 

[jostpuur]

will the pressure of the fluid play the role of the 4th component of the four vector?

You would probably need to deal with the stress-energy tensor, which is a 2nd-rank tensor, instead of with some four component object.

 

[quantumfireball]

i didnt know it would be so complicated
has anyone written a paper on this?
please elaborate on why to use a tensor?

 

[olgranpappy]

relativistic hydrodynamics of well known. so is quantizing density fluctuations of a fluid. one proceeds in the usual way by reducing the system to normal modes and quantizing those. I guess the relativistic quantum fluid is a bit harder, but there seem to be a few papers on it.

also, people use relativistic hydrodynamics to simulate nuclear collisions at the relativistic heavy ion collider with some degree of success.

 

[jostpuur]

relativistic hydrodynamics of well known. so is quantizing density fluctuations of a fluid. one proceeds in the usual way by reducing the system to normal modes and quantizing those. I guess the relativistic quantum fluid is a bit harder, but there seem to be a few papers on it.

also, people use relativistic hydrodynamics to simulate nuclear collisions at the relativistic heavy ion collider with some degree of success.

What are normal modes with fluids?

 

[Marco_84]

I think guys that the problem (the worst one) is that our equations display a non linear dynamics----> all our theories about normal modes fail... we can't use such a decomposition... i think that works only for small perturbation of the fields involved...
regards;
marco;

 

[Lazer Beam]

In this regard, consider the work of Joseph Hirschfelder et al circa 197Os.