## The Universe in a Helium DropletThere are fundamental relations between three vast areas of physics: particle physics, cosmology and condensed matter physics. The fundamental links between the first two areas, in other words, between micro- and macro-worlds, have been well established. There is a unified system of laws governing the scales from subatomic particles to the Cosmos and this principle is widely exploited in the description of the physics of the early Universe. The main goal of this book is to establish and define the connection of these two fields with condensed matter physics. According to the modern view, elementary particles (electrons, neutrinos, quarks, etc.) are excitations of a more fundamental medium called the quantum vacuum. This is the new 'aether' of the 21st Century. Electromagnetism, gravity, and the fields transferring weak and strong interactions all represent different types of the collective motion of the quantum vacuum. Among the existing condensed matter systems, a quantum liquid called superfluid 3He-A most closely represents the quantum vacuum. Its quasiparticles are very similar to the elementary particles, while the collective modes of the liquid are very similar to electromagnetic and gravitational fields, and the quanta of these collective modes are analogues of photons and gravitons. The fundamental laws of physics, such as the laws of relativity (Lorentz invariance) and gauge invariance, arise when the temperature of the quantum liquid decreases. This book is written for graduate students and researchers in all areas of physics. |

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### Contents

GUT and antiGUT | 1 |

QUANTUM BOSE LIQUID | 9 |

QUANTUM FERMIONIC LIQUIDS | 63 |

TOPOLOGICAL DEFECTS | 157 |

ANOMALIES OF CHIRAL VACUUM | 233 |

FERMIONS ON TOPOLOGICAL OBJECTS AND BRANE WORLD | 273 |

NUCLEATION OF QUASIPARTICLES AND TOPOLOGICAL DEFECTS | 319 |

VACUUM ENERGY AND VACUUM IN NONTRIVIAL GRAVITATIONAL BACKGROUND | 367 |

469 | |

499 | |

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### Common terms and phrases

ˆl-vector A-phase analog anomaly atoms axis B-phase baryonic black hole Bose bosonic brane Casimir chemical potential chiral fermions co-dimension co-dimension dc condensed matter corresponds cosmic strings cosmological constant counterflow Dirac domain wall effective theory electroweak energy spectrum equation equilibrium ergoregion Fermi points Fermi surface fermion zero modes fermionic charge frame gauge field gravity Hamiltonian hedgehog horizon inner observer instability interaction interface Landau Lett Lorentz low-energy corner magnetic field magnetic monopole mass massless microscopic momentum space monopole non-zero normal component nucleation obtained order parameter particles phase transition Phys physics Planck energy Planck scale quantized quantum liquids quantum vacuum quasiparticles relativistic rotating RQFT singular skyrmion soliton spacetime speed of light spin Standard Model superconductors superfluid superfluid 3He superfluid vacuum superfluid velocity superfluid-comoving symmetry temperature topological charge topological invariant trans-Planckian universality class vacua vacuum energy vector vierbein vortex core vortices winding number