Date: May 31 (Tue)
Time: 13:30 -
Place: Main Research bldg. 433
Speaker: Pablo A. Morales (University of Tokyo)
Title: Field theory of the perfect fluid
Abstract: In spite of its long history, fluid mechanics still lacks of an unconstrained action principle and as consequence, its field theoretical formulation remains incomplete. Problems arises when addressing rotational flow; the action the requires parametrizating the velocity field in terms of scalar gradients known as Clebsch potentials. Such parametrization is constraint-added and suffers from excessive degrees of freedom. In addition, the physical interpretation of the potential variables themselves is still controversial; Lagrange-coordinate variables, Chern-Simon like gauge are among the candidates.
In this talk, we propose a self-consistent formulation that settles ambiguities in the field theoretical description of the perfect fluid. In this way, the proliferation of the potential variables is not only natural but free from redundant degrees of freedom; only half of the scalar variables required in the conventional formalism, where the other half are reproduced as canonical conjugate quantities. As a natural consequence, constraints on mass, entropy, and Clebsch potentials do not appear. Within this formulation a natural generalization to the Clebsch parametrization is obtained, introducing to a new type of interactions on the fluid. This leads to interactions of 2 types; one is the gauge interaction on the Clebsch potentials, which yields the non-Abelian (Abelian) fluid dynamics in a pure manner. The other is the interaction on the velocity potentials, which convert the rest-mass energy to energies of other fields and vice-versa.
