Consequences of spontaneous and anomalous symmetry breaking for the orbital and mass flow hydrodynamics of helium-

In this thesis we address three problems associated with the mass flow and orbital hydrodynamics of $sp3$He-A. The first concerns the form of the T = 0 mass current in local equilibrium; the second is a paradox associated with the non-conservation of superfluid linear momentum at T = 0; and the third involves a longstanding disagreement between past calculations of the intrinsic orbital angular momentum in $sp3$He-A.;These problems are more fully described in chapter 1 along with a brief review of the generalized Hartree-Fock approach to the Bardeen-Cooper-Schrieffer theory of superconductivity. In chapter 2 we describe our formulation of the quasiparticle dynamics. In chapter 3 we demonstrate the occurrence of anomalous symmetry breaking in $sp3$He-A, and in chapter 4 we see how the first two problems can be understood as consequences of this anomalous symmetry breaking. In chapter 5 we calculate the intrinsic orbital angular momentum via a Berry phase argument and also through a calculation that is careful to account for backflow currents which are necessary for the maintenance of particle number conservation in the superfluid phase. On the basis of the latter calculation we propose an explanation for the disagreement in past calculations of the intrinsic orbital angular momentum in $sp3$He-A.