The universe in a helium droplet

Contents......Page 10
1 Introduction: GUT and anti-GUT......Page 24
I: QUANTUM BOSE LIQUID......Page 32
2.1 The Einstein theory of gravity......Page 34
2.2 Vacuum energy and cosmological term......Page 35
3.1 Theory of Everything in quantum liquids......Page 40
3.2 Weakly interacting Bose gas......Page 44
3.3 From Bose gas to Bose liquid......Page 50
4.1 Superfluid vacuum and quasiparticles......Page 55
4.2 Dynamics of superfluid vacuum......Page 59
4.3 Normal component – ‘matter’......Page 60
5.2 Energy–momentum tensor for ‘matter’......Page 65
5.3 Local thermal equilibrium......Page 68
5.4 Global thermodynamic equilibrium......Page 71
6.1 Non-locality in effective theory......Page 74
6.2 Effective vs microscopic theory......Page 79
6.3 Superfluidity and universality......Page 81
II: QUANTUM FERMIONIC LIQUIDS......Page 86
7.1 Introduction......Page 88
7.2 BCS theory......Page 89
7.3 Vacuum energy of weakly interacting Fermi gas......Page 93
7.4 Spin-triplet superfluids......Page 99
8 Universality classes of fermionic vacua......Page 109
8.1 Fermi surface as topological object......Page 110
8.2 Systems with Fermi points......Page 117
9.1 Fermions......Page 128
9.2 Effective electromagnetic field......Page 132
9.3 Effective SU(N) gauge fields......Page 137
10 Three levels of phenomenology of superfluid [sup(3)]He......Page 141
10.1 Ginzburg–Landau level......Page 142
10.2 London level in [sup(3)]He-A......Page 143
10.3 Low-temperature relativistic regime......Page 145
10.4 Parameters of effective theory in London limit......Page 151
10.5 How to improve quantum liquid......Page 153
11.1 Topological invariant for 2+1 systems......Page 158
11.2 2+1 systems with non-trivial p-space topology......Page 159
11.3 Fermi point as diabolical point and Berry phase......Page 162
11.4 Quantum phase transitions......Page 164
12.1 Momentum space topology of planar phase......Page 166
12.2 Quarks and leptons......Page 168
12.3 Momentum space topology of Standard Model......Page 172
12.4 Reentrant violation of special relativity......Page 176
III: TOPOLOGICAL DEFECTS......Page 180
13.1 Defects and homotopy groups......Page 182
13.2 Analogous ‘superfluid’ phases in high-energy physics......Page 185
14.1 Topology of [sup(3)]He-B defects......Page 188
14.2 Symmetry of defects......Page 194
14.3 Broken symmetry in B-phase vortex core......Page 201
15.1 [sup(3)]He-A and analogous phases in high-energy physics......Page 205
15.2 Singular defects in [sup(3)]He-A......Page 207
15.3 Fractional vorticity and fractional flux......Page 212
16.1 Hierarchy of energy scales and relative homotopy group......Page 218
16.2 Continuous vortices, skyrmions and merons......Page 222
16.3 Vortex sheet......Page 230
17.1 Monopoles terminating strings......Page 235
17.2 Defects at surfaces......Page 241
17.3 Defects on interface between different vacua......Page 244
IV: ANOMALIES OF CHIRAL VACUUM......Page 256
18 Anomalous non-conservation of fermionic charge......Page 258
18.1 Chiral anomaly......Page 259
18.2 Anomalous non-conservation of baryonic charge......Page 262
18.3 Analog of baryogenesis in [sup(3)]He-A......Page 264
18.4 Experimental check of Adler–Bell–Jackiw equation in [sup(3)]He-A......Page 271
19.1 Helicity in parity-violating systems......Page 274
19.2 Chern–Simons energy term......Page 275
19.3 Helical instability and ‘magnetogenesis’ due to chiral fermions......Page 278
20.1 Mixed axial–gravitational Chern–Simons term......Page 283
20.2 Orbital angular momentum in [sup(3)]He-A......Page 285
20.3 Odd current in [sup(3)]He-A......Page 286
21.1 Spin and statistics of skyrmions in 2+1 systems......Page 289
21.2 Quantized response......Page 292
V: FERMIONS ON TOPOLOGICAL OBJECTS AND BRANE WORLD......Page 296
22 Edge states and fermion zero modes on soliton......Page 298
22.1 Index theorem for fermion zero modes on soliton......Page 299
22.2 3+1 world of fermion zero modes......Page 306
23.1 Anomalous branch of chiral fermions......Page 311
23.2 Fermion zero modes in quasiclassical description......Page 318
23.3 Interplay of p- and r-topologies in vortex core......Page 323
24.1 Inertia of object moving in superfluid vacuum......Page 328
24.2 Fermion zero modes and vortex mass......Page 330
24.3 Associated hydrodynamic mass of a vortex......Page 332
25.1 Analog of Callan–Harvey mechanism of cancellation of anomalies......Page 335
25.2 Restricted spectral flow in the vortex core......Page 337
VI: NUCLEATION OF QUASIPARTICLES AND TOPOLOGICAL DEFECTS......Page 342
26.1 Landau critical velocity for quasiparticles......Page 344
26.2 Analog of pair production in strong fields......Page 348
26.3 Vortex formation......Page 351
26.4 Nucleation by macroscopic quantum tunneling......Page 355
27.1 Kelvin–Helmholtz instability in classical and quantum liquids......Page 362
27.2 Interface instability in two-fluid hydrodynamics......Page 369
28.1 Vortices and phase transitions......Page 374
28.2 Vortex formation at normal–superfluid interface......Page 381
VII: VACUUM ENERGY AND VACUUM IN NON-TRIVIAL GRAVITATIONAL BACKGROUND......Page 390
29.1 Analog of standard Casimir effect in condensed matter......Page 392
29.2 Interface between two different vacua......Page 395
29.3 Force on moving interface......Page 400
29.4 Vacuum energy and cosmological constant......Page 403
29.5 Mesoscopic Casimir force......Page 413
30.1 Surface of infinite red shift......Page 420
30.2 Conical space and antigravitating string......Page 427
31.1 Sagnac effect using superfluids......Page 429
31.2 Vortex, spinning string and Lense–Thirring effect......Page 431
31.3 Gravitational Aharonov–Bohm effect and Iordanskii force on a vortex......Page 435
31.4 Quantum friction in rotating vacuum......Page 439
32.1 Event horizons in vierbein wall and Hawking radiation......Page 447
32.2 Painlevé–Gullstrand metric in superfluids......Page 457
32.3 Horizon and singularity on AB-brane......Page 469
32.4 From ‘acoustic’ black hole to ‘real’ black hole......Page 475
33 Conclusion......Page 484
References......Page 492
C......Page 522
E......Page 524
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I......Page 527
M......Page 528
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R......Page 530
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V......Page 533
Z......Page 534