×

Electromagnetism as an emergent phenomenon: a step-by-step guide. (English) Zbl 1451.78002

Summary: We give a detailed description of electrodynamics as an emergent theory from condensed-matter-like structures, not only per se but also as a warm-up for the study of the much more complex case of gravity. We concentrate on two scenarios that, although qualitatively different, share some important features with the idea of extracting the basic generic ingredients that give rise to emergent electrodynamics and, more generally, to gauge theories. We start with Maxwell’s mechanical model for electrodynamics, where Maxwell’s equations appear as dynamical consistency conditions. We next take a superfluid \(^3\)He-like system as representative of a broad class of fermionic quantum systems whose low-energy physics reproduces classical electrodynamics (Dirac and Maxwell equations as dynamical low-energy laws). An important lesson that can be derived from both analyses is that the vector potential has a microscopic physical reality and only in the low-energy regime is this physical reality blurred in favor of gauge invariance, which in addition turns out to be secondary to effective Lorentz invariance.

MSC:

78A02 Foundations in optics and electromagnetic theory
82D50 Statistical mechanics of superfluids
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Rovelli C 2004 Quantum Gravity(Cambridge Monographs on Mathematical Physics) (Cambridge: Cambridge University Press) · Zbl 1091.83001 · doi:10.1017/CBO9780511755804
[2] Gambini R and Pullin J 2011 A First Course in Loop Quantum Gravity (Oxford: Oxford University Press) · Zbl 1243.83001 · doi:10.1093/acprof:oso/9780199590759.001.0001
[3] Thiemann T 2007 Modern Canonical Quantum General Relativity(Cambridge Monographs on Mathematical Physics) (Cambridge: Cambridge University Press) · Zbl 1129.83004 · doi:10.1017/CBO9780511755682
[4] Jacobson T 1995 Phys. Rev. Lett.75 1260-3 · Zbl 1020.83609 · doi:10.1103/PhysRevLett.75.1260
[5] Padmanabhan T 2010 AIP Conf. Proc.1241 93-108 · doi:10.1063/1.3462738
[6] Padmanabhan T 2010 Rept. Prog. Phys.73 046901 · doi:10.1088/0034-4885/73/4/046901
[7] Volovik G 2008 Phil. Trans. R. Soc. A 366 2935-51 · Zbl 1153.81544 · doi:10.1098/rsta.2008.0070
[8] Konopka T, Markopoulou F and Severini S 2008 Phys. Rev. D 77 104029 · doi:10.1103/PhysRevD.77.104029
[9] Barcelo C, Visser M and Liberati S 2001 Int. J. Mod. Phys. D 10 799-806 · Zbl 1155.83332 · doi:10.1142/S0218271801001591
[10] Volovik G 2003 The Universe in a Helium Droplet(International Series of Monographs on Physics) (Oxford: Clarendon) · Zbl 1140.83412
[11] Barcelo C, Garay L J and Jannes G 2011 Found. Phys.41 1532-41 · Zbl 1242.83033 · doi:10.1007/s10701-011-9577-9
[12] Polchinski J 1998 String Theory: Volume 1, An Introduction to the Bosonic String(Cambridge Monographs on Mathematical Physics) (Cambridge: Cambridge University Press) · Zbl 1006.81521
[13] Zwiebach B 2004 A First Course in String Theory A First Course in String Theory (Cambridge: Cambridge University Press) · Zbl 1072.81001 · doi:10.1017/CBO9780511841682
[14] Maxwell J 1861 Phil. Mag.21 161-75 · doi:10.1080/14786446108643033
[15] Maxwell J 1861 Phil. Mag.21 281-91 · doi:10.1080/14786446108643056
[16] Maxwell J 1861 Phil. Mag.21 338-48 · doi:10.1080/14786446108643067
[17] Maxwell J 1861 Phil. Mag.23 12-24 · doi:10.1080/14786446208643207
[18] Maxwell J 1861 Phil. Mag.23 85-95 · doi:10.1080/14786446208643219
[19] Longair S 2003 Theoretical Concepts in Physics: An Alternative View of Theoretical Reasoning in Physics (Cambridge: Cambridge University Press) · doi:10.1017/CBO9780511840173
[20] Dyson F 1999 Why is Maxwellʼs Theory so Hard to Understand? (Edinburgh: James Clerk Maxwell Foundation)
[21] Simpson T 1997 Maxwell on the Electromagnetic Field: A Guided Study(Masterworks of discovery: guided studies of great texts in science) (New Brunswick, NJ: Rutgers University Press)
[22] Moyer D F 1978 Stud. Hist. Phil. Sci. A 9 35-50 · Zbl 0378.01005 · doi:10.1016/0039-3681(78)90020-1
[23] Cat J 2001 Stud. Hist. Phil. Sci. B 32 395-441 · Zbl 1222.78002 · doi:10.1016/S1355-2198(01)00018-1
[24] Siegel D M 1992 Innovation in Maxwellʼs Electromagnetic Theory (Cambridge: Cambridge University Press) · doi:10.1017/CBO9780511529290
[25] Simpson T 2010 Maxwellʼs Mathematical Rhetoric: Rethinking the Treatise on Electricity and Magnetism (Santa Fe, NM: Green Lion Press)
[26] Rousseaux G and Guyon E 2002 Bull. Un. Phys.96 107-36
[27] Rousseaux G 2003 Ann. Fond. Louis de Broglie28 261-70 · Zbl 1329.78033
[28] Rousseaux G 2013 Eur. Phys. J. Plus128 81 · doi:10.1140/epjp/i2013-13081-5
[29] Leggett A J 1975 Rev. Mod. Phys.47 331-414 · doi:10.1103/RevModPhys.47.331
[30] Vollhardt D and Woelfle P 1990 The Superfluid Phases of Helium 3 (Oxford: Taylor & Francis)
[31] Leggett A 2006 Quantum Liquids: Bose Condensation and Cooper Pairing in Condensed-matter Systems(Oxford graduate texts in mathematics) (Oxford: Oxford University Press) · Zbl 1509.82002 · doi:10.1093/acprof:oso/9780198526438.001.0001
[32] Gor’kov L P 1959 Sov. Phys. JETP9 1364-7
[33] Horava P 2005 Phys. Rev. Lett.95 016405 · doi:10.1103/PhysRevLett.95.016405
[34] de Prato M, Pelissetto A and Vicari E 2004 Phys. Rev. B 70 214519 · doi:10.1103/PhysRevB.70.214519
[35] Gor’kov L 1958 Sov. Phys. JETP7 505-8
[36] Barceló C and Jannes G 2008 Found. Phys.38 191-9 · Zbl 1137.83306 · doi:10.1007/s10701-007-9196-7
[37] Mermin N D and Ho T L 1976 Phys. Rev. Lett.36 594-7 · doi:10.1103/PhysRevLett.36.594
[38] Ho T L and Mermin N D 1980 Phys. Rev. B 21 5190-7 · doi:10.1103/PhysRevB.21.5190
[39] Barceló C, Liberati S and Visser M 2005 Living Rev. Relativ.8 12 · Zbl 1255.83014 · doi:10.12942/lrr-2005-12
[40] Dalibard J, Gerbier F, Juzeliūnas G and Öhberg P 2011 Rev. Mod. Phys.83 1523-43 · doi:10.1103/RevModPhys.83.1523
[41] Jannes G 2009 Emergent gravity: the BEC paradigm PhD Thesis
[42] Carlip S 2014 Stud. Hist. Phil. Mod. Phys.46 200-8 · Zbl 1315.83024 · doi:10.1016/j.shpsb.2012.11.002
[43] Sindoni L 2012 SIGMA8 027 · Zbl 1242.83046
[44] Volovik G E 1998 Physica B 255 86-107 · doi:10.1016/S0921-4526(98)00456-6
[45] Jannes G and Volovik G E 2012 JETP Lett.96 215 · doi:10.1134/S0021364012160035
[46] Sakharov A D 1968 Sov. Phys.-Doklady12 1040
[47] Zel’dovich Y B 1967 Sov. J. Exp. Theor. Phys. Lett.6 345
[48] Jiménez J B and Maroto A L 2011 Mod. Phys. Lett. A 26 3025-39 · Zbl 1274.83157 · doi:10.1142/S0217732311037315
[49] Jenkins A 2006 Topics in particle physics and cosmology beyond the standard model PhD Thesis California Institute of Technology
[50] Wen X G 2001 Phys. Rev. Lett.88 011602 · doi:10.1103/PhysRevLett.88.011602
[51] Maccione L, Taylor A M, Mattingly D M and Liberati S 2009 J. Cosmol. Astropart. Phys.4 022 · doi:10.1088/1475-7516/2009/04/022
[52] Liberati S 2013 Class. Quantum Grav.30 133001 · Zbl 1273.83002 · doi:10.1088/0264-9381/30/13/133001
[53] Volovik G E 2006 From Quantum Hydrodynamics to Quantum Gravity (Singapore: World Scientific)
[54] Wölfle P 1976 Phys. Rev. Lett.37 1279-82 · doi:10.1103/PhysRevLett.37.1279
[55] Vollhardt D 1997 Pair Correlations in Superfluid Helium 3
[56] Cross M C 1975 J. Low Temp. Phys.21 525-34 · doi:10.1007/BF01141607
[57] Dziarmaga J 2002 Sov. J. Exp. Theor. Phys. Lett.75 273-7 · doi:10.1134/1.1481462
[58] Visser M 2002 Mod. Phys. Lett. A 17 977-91 · Zbl 1083.83544 · doi:10.1142/S0217732302006886
[59] Andreev A and Kagan M 1987 J. Exp. Theor. Phys.66 504
[60] Iliopoulos J, Nanopoulos D V and Tomaras T N 1980 Phys. Lett. B 94 141-4 · doi:10.1016/0370-2693(80)90843-6
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.