by G E Volovik (Landau Inst.)

This book discusses the unique properties of superfluid phases of ³He, the condensed matter with the outmost broken symmetry, which combine in a surprising way the properties of ordered magnets, liquid crystals and superfluids. The complicated vacuum state of these phases with a large number of fermionic and bosonic quasiparticles and topological objects remains the vacuum in modern quantum field theories. Some of the objects and physical phenomena in ³He have strong analogy with the neutrino, W-bosons, weak interactions, gravity, chiral anomaly, Quantum Hall Effect and fractional statistics. As an example of topological objects, the quantized vortices in ³He phases are discussed in detail, including singular and continuous vortices, half-quantum vortices, broken symmetry in the vortex core and phase transitions between the vortex states with different symmetry and topology.

• Introduction
• Broken Symmetry in Superfluid Phase of ³He
• Textures and Super-currents in Superfluid Phases of ³He
• Bose Excitations in Superfluid Phases of ³He
• Fermi Excitations in Superfluid Phases of ³He
• Orbital Dynamics and Anomalies in Quantum Field Theory
• Topological Objects in Superfluid Phases of ³He
• Spontaneous Symmetry Breaking in the ³He Vortices
• Quasi-Two-Dimensional Superfluid ³He: Fractional Charge, Spin and Statistics
• Conclusion