Symmetry Breaking using Fluids II: Velocity Potential Method

Abstract

A generalization of scalar electrodynamics called fluid electrodynamics is presented. In this theory a fluid replaces the Higgs scalar field. Fluid electrodynamics might have application to the theory of low temperature Helium superfluids, but here it is argued that it provides an alternative method of approaching symmetry breaking in particle physics. The method of constructing fluid electrodynamics is to start with the velocity decomposition of a perfect fluid as in general relativity. A unit vector tangent to the flow lines of an isentropic fluid can be written in terms of scalar potentials: $V_a=h^{-1}(\ph_a+\al\bt_a-þS)$. A novel interacting charged fluid can be obtained by applying the covariant derivative: $D_a=\p_a+ieA_a$ to these scalar potentials. This fluid is no longer isentropic and there are choices for which it either obeys the second law of thermodynamics or not. A mass term of the correct sign occurs for the $A$ term in the stress, and this mass term depends on the potentials in the above vector. The charged fluid can be reduced to scalar electrodynamics and the standard approach to symmetry breaking applied; alternatively a mass can be induced by the fluid by using just the thermodynamic potentials and then fixing at a critical point, if this is taken to be the Bose condensation point then the induced mass is negligible.