<p>In analogy with the non-Abelian gauge helicities conserved in time for “null fields”, that we have defined previously, in this paper we first define non-Abelian fluid helicities and then total non-Abelian helicities for combined non-Abelian fluid and gauge fields. For a U(N) group the helicities considered are for both gluonic-type fluids, composed of particles in the adjoint representation, and quark-type fluids, in the <i>N</i>-dimensional Cartan subalgebra. We write down various Lagrangian formulations for the uncoupled and coupled systems. In each case we determine the equations of motion, symmetries, and a Hamiltonian formulation. Taking the velocity of the fluid in the adjoint representation, we find that in the case of the gluonic fluid, we can write a non-Abelian gluonic fluid Euler-Yang-Mills equation that conserves the defined helicities, and comes from a Lagrangian.</p>

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Nonabelian fluids and helicities

  • Horatiu Nastase,
  • Jacob Sonnenschein

摘要

In analogy with the non-Abelian gauge helicities conserved in time for “null fields”, that we have defined previously, in this paper we first define non-Abelian fluid helicities and then total non-Abelian helicities for combined non-Abelian fluid and gauge fields. For a U(N) group the helicities considered are for both gluonic-type fluids, composed of particles in the adjoint representation, and quark-type fluids, in the N-dimensional Cartan subalgebra. We write down various Lagrangian formulations for the uncoupled and coupled systems. In each case we determine the equations of motion, symmetries, and a Hamiltonian formulation. Taking the velocity of the fluid in the adjoint representation, we find that in the case of the gluonic fluid, we can write a non-Abelian gluonic fluid Euler-Yang-Mills equation that conserves the defined helicities, and comes from a Lagrangian.