Contents. Goldstone Bosons in 3HeA Soft Modes Dynamics and Lie Algebra of Group G:


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2 ... Vlll Contents 3. Textures and Supercurrents in Superfluid Phases of 3He 3.1. Textures, Gradient Energy and Rigidity 3.2. Why Superfuids are Superfluid 3.3. Superfluidity and Response to a Transverse Gauge Field 3.4. Nonpotential Superflow in 3HeA 3.5. Perpetuum Motion of the Aphase 3.6. Textural Energy and Supercurrent in 3HeA 3.7. Spin Soliton in 3HeA 3.8. Order Parameter Textures 3.9. Coherence Length and London Limit Disgyrations and Vortex. London Equations for the Orbital Texture Disgyrations and Vortex. Singularity in the Degeneracy Parameters Radial Disgyration. The Hard Core Structure Pure Vortices. The Hard Core Structure AB Interface. Symmetry and Structure Symmetry of the AB Interface and Boundary Conditions 4. Bose Excitations in Superfluid Phases of 3He Goldstone Bosons in 3HeA Soft Modes Dynamics and Lie Algebra of Group G: Spin Waves. Goldstone and QuasiGoldstone Nuclear Magnetic Resonance in 3HeA NMR on Textures in 3HeA Vacuum Symmetry H and Quantum Numbers of Bose and Fermi Excitations in 3HeA Bosonic Collective Modes in 3He and Irreducible Representations of Group H Bosonic Collective Modes in 3HeB Dynamics of the Goldstone Fields in 3HeB Superfluid Hydrodynamics in 3HeB Goldstone Bosons in 3HeB
3 Contents 5. Fermi Excitations in Superfluid Phases of 3He 5.1. BogoliubovNambu Matrix for Fermions in Paircorrelated Fermi Systems 5.2. Quasiparticles in Conventional Superconductors 5.3. Representation f and the Order P 5.4. Quasiparticle Spctrum in 5.5. Bogoliubov Hamiltonian for Quasiparticles in 3HeB vs. Dirac Hamiltonian for Electrons 5.6. Lorentz Symmetry as Combined Symmetry, View from 3HeB 5.7. Breaking of the Relative Lorentz Symmetry 5.8. Gap Nodes in the Quasiparticle Spectrum of 3HeA Class of Intermediate Superfluids 5.9. Combined Gauge Symmetry and Gap Nodes Stability of Gap Nodes in the Aphase Spectrum Near the Fermi Points and Relativistic Massless Particles Lefthanded and Righthanded Fermions Near the Fermi Points Spinorbit Waves and W Bosons Mass of the W Bosons is Zero in the BCS Theory of 3HeA Hidden Symmetry in the Aphase Origin of the W Boson Mass in 3HeA Gravitons in 3HeA Cosomological Term in the Einstein Equations, View from 3HeA ix Orbital Dynamics and Anomalies in Quantum Field Theory 6.1. Lie Algebra of Poisson Brackets for Aphase Orbital Dynamics 98 98
4 X Contents 6.2. Anomaly Cancellation as Lifshitz Transition 6.3. The Anomalyfree Equations for Orbital Dynamics 6.4. Phase Slippage Through the Dynamics of the Orbital Vector 6.5. Gap Nodes Contributions to the Orbital Dynamics 6.6. Anomaly in Orbital Dynamics and Chiral Anomaly 6.7. Spectrum of the Chiral Fermions in Magnetic Field 6.8. Anomalous Branch and Nonzero Density of States, Zero Charge Effect and Nonanalyticity of the Magnetic Energy of the Vacuum Nonanalytic London Energy of the 3He Vacuum ChiraI Anomaly and Nonconservationn of the Vacuum Current Dissipation in the Orbital Motion at Zero Temperature and Pair Creation in Electric Field in Particle Physics WessZumino Action for the Orbital Dynamics Internal Angular Momentum of the Aphase and the Mass of Photon Pair Creation by Accelerated Object and the Unruh Effect Topological Objects in Superfluid Phases of 3He Quantum Number and Topological Charge Topological and Symmetry Classification Schemes of Textures Halfquantum Vortex and Combined Invariance Topological Classification of the Linear Defects Topology of Linear Defects in the Aphase Unwinding of the Singularity in the Doubly Quantized Vortex Parity Breaking in the Continuous Vortex Topology of the Continuous Textures. Second Homotopy Group 7.9. Topological Phase Transition in Continuous Vortices
5 Contents xi Monopole and Boojum. Relative Homotopy Group Topology of Vortices and Disclinations in the Bphase Soliton Terminating on the Disclination in the Bphase Topological Confinement of the Defects in Superfluid 3He Stabilization of the VortexDisclination with the Solitonic Tail in the Rotating Vessel Spontaneous Symmetry Breaking in the 3He Vortices Compulsory and Spontaneous Symmetry Breaking in Inhomogeneous Vacuum Symmetry of Linear Defects Symmetry of Vortices in 3HeB The Most Symmetric Vortices in 3HeB Vortices Broken Parity in 3HeB Vortices Aphase Core of the 3HeB Vortex 8.7. Planar Phase vs. Aphase in the Core of the 3HeB Vortex 8.8. Broken Axisymmetry in 3HeB vortex. Molecule of Halfquantum Vortices 8.9. Physical Properties of the Vortices with Broken Symmetry QuasiTwoDimensional Superfluid 3He: Fractional Charge, Spin and Statistics Quasitwodimensional Objects in Superfluid 3He Superfluid Phases in Thin Films Generations of Fermions Symmetry and Internal Topology of Ground State Topological Invariant for the Fermi Point Topological Invariant in Terms of the Green s Function Topology of the Ground State of the 3He Film Adiabatical Process, Conservation of Topological Invariant and Diabolical Points
6 xii Contents Quantum Statistics of Solitons in the 3He Film and Orbital Ferromagnetism Spin Current QHE in Superfluid 3HeA Films Topological Quantization in Other Superfluid Phases of 3He Films Conclusion 207 References 211
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