×
Hehl, Friedrich W.; Itin, Yakov; Obukhov, Yuri N.

On Kottler’s path: origin and evolution of the premetric program in gravity and in electrodynamics. (English) Zbl 1351.78003

Int. J. Mod. Phys. D 25, No. 11, Article ID 1640016, 37 p. (2016).
Summary: In 1922, F. Kottler put forward the program to remove the gravitational potential, the metric of spacetime, from the fundamental equations in physics as far as possible [Wien. Ber. 131, 119–146 (1922; JFM 48.1034.01) and ibid. 131, 1–14 (1922; JFM 48.1033.02)]. He successfully applied this idea to Newton’s gravitostatics and to Maxwell’s electrodynamics, where Kottler recast the field equations in premetric form and specified a metric-dependent constitutive law. We will discuss the basics of the premetric approach and some of its beautiful consequences, like the division of universal constants into two classes. We show that classical electrodynamics can be developed without a metric quite straightforwardly: the Maxwell equations, together with a local and linear response law for electromagnetic media, admit a consistent premetric formulation. Kottler’s program succeeds here without provisos. In Kottler’s approach to gravity, making the theory relativistic, two premetric quasi-Maxwellian field equations arise, but their field variables, if interpreted in terms of general relativity, do depend on the metric. However, one can hope to bring the Kottler idea to work by using the teleparallelism equivalent of general relativity, where the gravitational potential, the coframe, can be chosen in a premetric way.

Cited in 4 Documents

MSC:

78A25 Electromagnetic theory (general)
83C50 Electromagnetic fields in general relativity and gravitational theory
78A40 Waves and radiation in optics and electromagnetic theory

Keywords:

premetric electrodynamics; quasi-Maxwellian gravitodynamics; teleparallelism; two classes of universal constants

Citations:

JFM 48.1034.01; JFM 48.1033.02
Cite Review PDF
Full Text: DOI arXiv

References:

[1] 1. D. van Dantzig, Helv. Phys. Acta4 (1956) 48.
[2] 2. F. Kottler, Sitzungsber. Akad. Wiss. Wien, Math.-Nat. Kl. Abt. IIa, 131 (1922) 1.
[3] 3. F. Kottler, Sitzungsber. Akad. Wiss. Wien, Math.-Nat. Kl. Abt. IIa, 131 (1922) 119.
[4] 4. E. Whittaker, A History of the Theories of Aether and Electricity, Vol. 1: The Classical Theories (first published 1910 and revised and enlarged 1951), Vol. 2: The Modern Theories 1900-1926 (first published 1953). Reprinted as two volumes (Humanities Press, New York, 1973).
[5] 5. D. van Dantzig, Proc. Camb. Philos. Soc.30 (1934) 421. genRefLink(16, ’S0218271816400162BIB005’, ’10.1017
[6] 6. D. van Dantzig, Kon. Akad. Wettensch. Amsterdam37 (1934) 522, 526, 643, 825; ibid.39 (1936) 126.
[7] 7. D. van Dantzig, Erkenntnis7 (1937/1938) 142. genRefLink(16, ’S0218271816400162BIB007’, ’10.1007
[8] 8. J. L. Flowers and B. W. Petley, Rep. Progr. Phys.64 (2001) 1191. genRefLink(16, ’S0218271816400162BIB008’, ’10.1088
[9] 9. P. J. Mohr, B. N. Taylor and D. B. Newell, Rev. Mod. Phys.84 (2012) 1527. genRefLink(16, ’S0218271816400162BIB009’, ’10.1103
[10] 10. P. J. Mohr, D. B. Newell and B. N. Taylor, arXiv:1507.07956 [arXiv] ; [http://www.physics.nist.gov/constants] .
[11] 11. R. Fleischmann, Z. Naturf.26a (1971) 331. genRefLink(64, ’S0218271816400162BIB011’, ’1971ZNatA..26..331F’);
[12] 12. J. A. Schouten, Tensor Analysis for Physicists, 2nd edn. (Dover, Mineola, New York, 1989). · Zbl 0044.38302
[13] 13. P. Bamberg and S. Sternberg, A Course in Mathematics for Students of Physics, Vol. 2 (Cambridge University Press, Cambridge, UK, 1990). · Zbl 0706.00002
[14] 14. F. Scheck, Classical Field Theory, on Electrodynamics, Non-Abelian Gauge Theories and Gravitation (Springer, Heidelberg, 2012). · Zbl 1246.83001
[15] 15. O. Heaviside, The Electrician31 (1893) 281, 359; reprinted in Electromagnetic Theory, Vol. 1 (AMS Chelsea Publishing, Providence, Rhode Island, 2003), pp. 455.
[16] 16. F. Kottler, Ann. Phys. (Berlin)361 (1918) 401. genRefLink(16, ’S0218271816400162BIB016’, ’10.1002
[17] 17. F. Kottler, http://alberteinstein.info/.
[18] 18. P. Havas, Einstein, Relativity and Gravitation Research in Vienna before 1938, in The Expanding Worlds of General Relativity (Birkhäuser, Boston, MA, 1999), pp. 161-206. genRefLink(16, ’S0218271816400162BIB018’, ’10.1007 · Zbl 0943.83501
[19] 19. H. Goenner, J. Renn, J. Ritter and T. Sauer (eds.), The Expanding Worlds of General Relativity, Einstein Studies, Vol. 7 (Birkhäuser, Boston, MA, 1999). genRefLink(16, ’S0218271816400162BIB019’, ’10.1007 · Zbl 0924.00026
[20] 20. F. Kottler, [http://gedenkbuch.univie.ac.at/] .
[21] 21. M. M. G. Ricci and T. Levi-Civita, Math. Ann.54 (1900) 125. genRefLink(16, ’S0218271816400162BIB021’, ’10.1007
[22] 22. C. Truesdell and R. A. Toupin, The Classical Field Theories. Encyclopedia of Physics, ed. S. Flügge, Vol. 3/1 (Berlin, Springer, 1960), pp. 226-793.
[23] 23. P. Russer, Electromagnetics, Microwave Circuit and Antenna Design for Communications Engineering, 2nd edn. (Artech House, Norwood, MA, 2006). · Zbl 1066.78001
[24] 24. E. Tonti, The Mathematical Structure of Classical and Relativistic Physics, A General Classification Diagram (Birkhäuser, New York, 2013). genRefLink(16, ’S0218271816400162BIB024’, ’10.1007 · Zbl 1298.00082
[25] 25. F. Gronwald, F. W. Hehl and J. Nitsch, arXiv:physics/0506219 [arXiv] .
[26] 26. J. Wallot, Grössengleichungen, Einheiten und Dimensionen (Quantity Equations, Units, and Dimensions, in German) (Barth, Leipzig, 1953).
[27] 27. U. Stille, Messen und Rechnen in der Physik – Grundlagen der Grösseneinführung und Einheitenfestlegung (Vieweg, Braunschweig, 1961). · Zbl 0064.17903
[28] 28. J. Flowers, Science306 (2004) 1324. genRefLink(16, ’S0218271816400162BIB028’, ’10.1126
[29] 29. J. D. Jackson, Classical Electrodynamics, 3rd edn. (Wiley, NY, 1999).
[30] 30. N. Carron, arXiv:1506.01951.
[31] 31. F. W. Hehl and Y. N. Obukhov, Foundations of Classical Electrodynamics: Charge, Flux, and Metric (Birkhäuser, Boston, MA, 2003). genRefLink(16, ’S0218271816400162BIB031’, ’10.1007 · Zbl 1032.78001
[32] 32. E. J. Post, Action as Pseudoscalar (unpublished), private communication around 2000.
[33] 33. F. W. Hehl and Y. N. Obukhov, Gen. Relativ. Gravit.37 (2005) 733. genRefLink(16, ’S0218271816400162BIB033’, ’10.1007
[34] 34. D. Andreone, Recent Advances in Metrology and Fundamental Constants (Varenna, Italy, 2000), pp. 317-348.
[35] 35. B. D. Josephson, Phys. Lett.1 (1962) 251. genRefLink(16, ’S0218271816400162BIB035’, ’10.1016
[36] 36. B. Jeckelmann, The quantum Hall effect and its application in metrology, in Recent Advances in Metrology and Fundamental Constants (IOS Press, Amsterdam, 2001), pp. 263-290.
[37] 37. K. von Klitzing, G. Dorda and M. Pepper, Phys. Rev. Lett.45 (1980) 494. genRefLink(16, ’S0218271816400162BIB037’, ’10.1103
[38] 38. D. Haddad et al., Rev. Sci. Instrum.87 (2016) 061301. genRefLink(16, ’S0218271816400162BIB038’, ’10.1063
[39] 39. A. F. Milone and P. Giacomo (eds.), Metrology and Fundamental Constants, Proc. Int. School of Phys. ”E. Fermi” (Varenna, Italy, 1976), Course 68 (North-Holland, Amsterdam, 1980).
[40] 40. T. J. Quinn and S. Leschiutta (eds.), Recent Advances in Metrology and Fundamental Constants, Proc. Int. School of Phys. ”E. Fermi” (Varenna, Italy, 2000), Course 146 (IOS Press, Amsterdam, 2001).
[41] 41. J. Weis and K. von Klitzing, Philos. Trans. Roy. Soc. A369 (2011) 3954. genRefLink(16, ’S0218271816400162BIB041’, ’10.1098
[42] 42. S. Bieri and J. Fröhlich, Comptes Rendus Phys.12 (2011) 332. genRefLink(16, ’S0218271816400162BIB042’, ’10.1016
[43] 43. E. O. Göbel and U. Siegner, Quantum Metrology: Foundation of Units and Measurements (Wiley-VCH, Weinheim, Germany, 2015). genRefLink(16, ’S0218271816400162BIB043’, ’10.1002
[44] 44. C. Kiefer, Quantum Gravity, 3rd edn. (Oxford University Press, Oxford, 2012).
[45] 45. F. W. Hehl, Y. N. Obukhov and B. Rosenow, Phys. Rev. Lett.93 (2004) 096804. genRefLink(16, ’S0218271816400162BIB045’, ’10.1103
[46] 46. G. Yu. Bogoslovsky, Nuovo Cim. B40 (1977) 99, 116. genRefLink(16, ’S0218271816400162BIB046’, ’10.1007
[47] 47. G. Yu. Bogoslovsky and H. F. Goenner, Gen. Relativ. Gravit.31 (1999) 1565. genRefLink(16, ’S0218271816400162BIB047’, ’10.1023
[48] 48. T. H. O’Dell, The Electrodynamics of Magneto-Electric Media (North-Holland, Amsterdam, 1970).
[49] 49. A. Einstein, Sitzungsber. Königl. Preuss. Akad. Wiss.Berlin (1916) 184-188; The Collected Papers of Albert Einstein, Vol. 6, eds. A.J. Kox et al. (Princeton University Press, Princeton, 1996), pp. 263-269.
[50] 50. A. Einstein, The Meaning of Relativity, 5th edn. (Princeton University Press, Princeton, NJ, 1955). · Zbl 0067.20404
[51] 51. A. Einstein, Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen, in Jahrbuch der Radioaktivität und Elektronik (Hirzel, Leipzig, 1907), pp. 411-462.
[52] 52. N. Dadhich, Int. J. Mod. Phys. D20 (2011) 2739. [Abstract] genRefLink(128, ’S0218271816400162BIB052’, ’000300432600005’); genRefLink(64, ’S0218271816400162BIB052’, ’2011IJMPD..20.2739D’);
[53] 53. T. Sauer, Ann. Phys. (Berlin)524 (2012) A135. genRefLink(16, ’S0218271816400162BIB053’, ’10.1002
[54] 54. D. Braun, F. Schneiter and U. R. Fischer, arXiv:1502.04979 [arXiv] .
[55] 55. SI Brochure: The International System of Units (SI), Bureau International des Poids et Mesures, Sèvres, France [8th edn., 2006; updated in 2014], [http://www.bipm.org/en/publications/si-brochure/] .
[56] 56. S. Deser, Am. J. Phys.73 (2005) 752. genRefLink(16, ’S0218271816400162BIB056’, ’10.1119
[57] 57. S. Deser and F. A. E. Pirani, Ann. Phys. (NY)43 (1967) 436. genRefLink(16, ’S0218271816400162BIB057’, ’10.1016
[58] 58. I. Newton, Original letter from Isaac Newton to Richard Bentley, [http://www.newtonproject.sussex.ac.uk/view/texts/normalized/THEM00258] .
[59] 59. N. T. Roseveare, Mercury’s Perihelion – From Le Verrier to Einstein (Clarendon Press, Oxford, UK, 1982). · Zbl 0482.01014
[60] 60. G. Holzmüller, Zeitschr. f. Math. Phys.15 (1870) 69.
[61] 61. F. Tisserand, Compt. Rend. Acad. Sci. (Paris)75 (1872) 760.
[62] 62. F. Tisserand, Compt. Rend. Acad. Sci. (Paris)110 (1890) 313.
[63] 63. H. Thirring, Phys. Zeits.19 (1918) 204.
[64] 64. W. Rindler, Relativity – Special, General and Cosmological (Oxford University Press, Oxford, UK, 2001). · Zbl 0981.83001
[65] 65. M. Blagojević and F. W. Hehl (eds.), Gauge Theories of Gravitation, a Reader with Commentaries (Imperial College Press, London, 2013). [Abstract] · Zbl 1282.83046
[66] 66. Y. Itin, Class. Quantum Grav.19 (2002) 173. genRefLink(16, ’S0218271816400162BIB066’, ’10.1088
[67] 67. Y. N. Obukhov and J. G. Pereira, Phys. Rev. D67 (2003) 044016. genRefLink(16, ’S0218271816400162BIB067’, ’10.1103
[68] 68. J. W. Maluf, Ann. Phys. (Berlin)525 (2013) 339. genRefLink(16, ’S0218271816400162BIB068’, ’10.1002
[69] 69. L. Ryder, Introduction to General Relativity (Cambridge University Press, Cambridge, UK, 2009). genRefLink(16, ’S0218271816400162BIB069’, ’10.1017 · Zbl 1167.83301
[70] 70. B. F. Schutz, Gravity from the Ground Up (Cambridge University Press, Cambridge, UK, 2003). genRefLink(16, ’S0218271816400162BIB070’, ’10.1017
[71] 71. J. Boos, Int. J. Mod. Phys. D24 (2015) 1550079. [Abstract] genRefLink(128, ’S0218271816400162BIB071’, ’000359723100012’); genRefLink(64, ’S0218271816400162BIB071’, ’2015IJMPD..2450079B’);
[72] 72. S. J. Clark and R. W. Tucker, Class. Quantum Grav.17 (2000) 4125. genRefLink(16, ’S0218271816400162BIB072’, ’10.1088
[73] 73. R. T. Jantzen, P. Carini and D. Bini, Ann. Phys. (NY)215 (1992) 1. genRefLink(16, ’S0218271816400162BIB073’, ’10.1016
[74] 74. R. Maartens, Gen. Relativ. Gravit.40 (2008) 1203. genRefLink(16, ’S0218271816400162BIB074’, ’10.1007
[75] 75. R. Maartens and B. A. Bassett, Class. Quantum Grav.15 (1998) 705. genRefLink(16, ’S0218271816400162BIB075’, ’10.1088
[76] 76. B. Mashhoon, Gravitoelectromagnetism: A Brief Review, in The Measurement of Gravitomagnetism: A Challenging Enterprise, ed. L. Iorio (Nova Science, New York, 2007), pp. 29-39.
[77] 77. M. L. Ruggiero and A. Tartaglia, Nuovo Cimento. B117 (2002) 743. genRefLink(64, ’S0218271816400162BIB077’, ’2002NCimB.117..743R’);
[78] 78. E. Tonti (Trieste), Private Communication.
[79] 79. F. W. Hehl, Y. N. Obukhov, J. P. Rivera and H. Schmid, Phys. Rev. A77 (2008) 022106. genRefLink(16, ’S0218271816400162BIB079’, ’10.1103
[80] 80. H. Bateman, Proc. London Math. Soc. Ser.8(1) (1910) 375. genRefLink(16, ’S0218271816400162BIB080’, ’10.1112
[81] 81. I. E. Tamm, Zhurn. Ross. Fiz.-Khim. Ob.57 (1925) 209; reprinted in Collected Papers (Nauka, Moscow, 1975), pp. 33-61.
[82] 82. E. J. Post, Formal Structure of Electromagnetics – General Covariance and Electromagnetics (North Holland, Amsterdam, 1962, and Dover, Mineola, NY, 1997).
[83] 83. E. J. Post, Found. Phys.9 (1979) 619. genRefLink(16, ’S0218271816400162BIB083’, ’10.1007
[84] 84. A. Serdyukov, I. Semchenko, S. Tretyakov and A. Sihvola, Electromagnetics of Bi-anisotropic Materials, Theory and Applications (Gordon and Breach, Amsterdam, 2001).
[85] 85. I. V. Lindell, Differential Forms in Electromagnetics (IEEE Press, Piscataway, NJ, and Wiley-Interscience, 2004). genRefLink(16, ’S0218271816400162BIB085’, ’10.1002 · Zbl 1080.78001
[86] 86. I. V. Lindell, Prog. Electromagn. Res.54 (2005) 321. genRefLink(16, ’S0218271816400162BIB086’, ’10.2528
[87] 87. I. V. Lindell, Multiforms, Dyadics and Electromagnetic Media (Wiley, Hoboken, NJ (and IEEE Press), 2015). genRefLink(16, ’S0218271816400162BIB087’, ’10.1002
[88] 88. A. Favaro, Recent Advances in Classical Electromagnetic Theory, Ph.D. thesis, Imperial College London, 2012, [https://spiral.imperial.ac.uk/handle/10044/1/10482] .
[89] 89. W. T. Ni, Int. J. Mod. Phys. D25 (2016) 1630002. [Abstract] genRefLink(128, ’S0218271816400162BIB089’, ’000371308700002’); genRefLink(64, ’S0218271816400162BIB089’, ’2016IJMPD..2530002N’);
[90] 90. C. Pfeifer and D. Siemssen, Phys. Rev. D93 (2016) 105046. genRefLink(16, ’S0218271816400162BIB090’, ’10.1103
[91] 91. E. Schmutzer, Relativistische Physik (klassische Theorie) (Geest & Portig, Leipzig, 1968).
[92] 92. A. B. Balakin, Symmetry (MDPI)8 (2016) 56. genRefLink(16, ’S0218271816400162BIB092’, ’10.3390
[93] 93. A. B. Balakin and V. A. Popov, Phys. Rev. D92 (2015) 105025. genRefLink(16, ’S0218271816400162BIB093’, ’10.1103
[94] 94. D. H. Delphenich, Ann. Phys. (Berlin)16 (2007) 207. genRefLink(16, ’S0218271816400162BIB094’, ’10.1002
[95] 95. D. H. Delphenich, Pre-metric Electromagnetism (2009), p. 410 pages, [http://www.neo-classical-physics.info/] . · Zbl 1179.78008
[96] 96. D. Delphenich, arXiv:1512.05183 [arXiv] .
[97] 97. F. Cabral and F. S. N. Lobo, arXiv:1602.01492; arXiv:1603.08180; arXiv:1603.08157.
[98] 98. R. C. Rumpf, Solid State Phys.40 (2015) 213.
[99] 99. Y. Zhang, L. Shi and C. Xie, Opt. Lett.41 (2016) 3070. genRefLink(16, ’S0218271816400162BIB099’, ’10.1364
[100] 100. C. A. A. de Carvalho, Phys. Rev. D93 (2016) 105005. genRefLink(16, ’S0218271816400162BIB100’, ’10.1103
[101] 101. F. W. Hehl and Y. N. Obukhov, Phys. Lett. A334 (2005) 249. genRefLink(16, ’S0218271816400162BIB101’, ’10.1016
[102] 102. Y. N. Obukhov and F. W. Hehl, Phys. Lett. A341 (2005) 357. genRefLink(16, ’S0218271816400162BIB102’, ’10.1016
[103] 103. F. W. Hehl, Y. N. Obukhov, J. P. Rivera and H. Schmid, Phys. Lett. A372 (2008) 1141. genRefLink(16, ’S0218271816400162BIB103’, ’10.1016
[104] 104. F. W. Hehl, Y. N. Obukhov, J. P. Rivera and H. Schmid, Eur. Phys. J. B71 (2009) 321. genRefLink(16, ’S0218271816400162BIB104’, ’10.1140
[105] 105. A. M. Essin, J. E. Moore and D. Vanderbilt, Phys. Rev. Lett.102 (2009) 146805. genRefLink(16, ’S0218271816400162BIB105’, ’10.1103
[106] 106. S. Seki et al., Phys. Rev. Lett.115 (2015) 266601. genRefLink(16, ’S0218271816400162BIB106’, ’10.1103
[107] 107. I. V. Lindell, A. Sihvola and A. Favaro, arXiv:1604.04416 [arXiv] .
[108] 108. A. Rosch (Cologne), private communication (May 2016).
[109] 109. R. B. Versteeg et al., arXiv:1605.01900 [arXiv] .
[110] 110. W.-T. Ni, [http://astrod.wikispaces.com/] .
[111] 111. W.-T. Ni, Phys. Rev. Lett.38 (1977) 301. genRefLink(16, ’S0218271816400162BIB111’, ’10.1103
[112] 112. A. B. Balakin, Phys. Rev. D94 (2016) 024021. genRefLink(16, ’S0218271816400162BIB112’, ’10.1103
[113] 113. L. Wu et al., arXiv:1603.04317 [arXiv] .
[114] 114. F. R. Prudêncio, S. A. Matos and C. R. Paiva, IEEE Trans. Microwave Theory Technol.62 (2014) 1417. genRefLink(16, ’S0218271816400162BIB114’, ’10.1109
[115] 115. V. H. Rumsey, Phys. Rev.94 (1954) 1483. genRefLink(16, ’S0218271816400162BIB115’, ’10.1103
[116] 116. E. O. Kamenetskii, Microwave Opt. Technol. Lett.19 (1998) 412. genRefLink(16, ’S0218271816400162BIB116’, ’10.1002
[117] 117. P. R. McIsaac, IEEE Trans. Microwave Theory Tech.27 (1979) 340. genRefLink(16, ’S0218271816400162BIB117’, ’10.1109
[118] 118. H. B. G. Casimir, Rev. Mod. Phys.17 (1945) 343. genRefLink(16, ’S0218271816400162BIB118’, ’10.1103
[119] 119. L. Onsager, Phys. Rev.37 (1931) 405; Phys. Rev.38 (1931) 2265.
[120] 120. G. T. Rado, Phys. Rev. B8 (1973) 5239. genRefLink(16, ’S0218271816400162BIB120’, ’10.1103
[121] 121. S. Tretyakov, A. Sihvola and B. Jancewicz, J. Electromag. Waves Appl.16 (2002) 573. genRefLink(16, ’S0218271816400162BIB121’, ’10.1163
[122] 122. A. Lakhtakia and R. A. Depine, AEU Int. J. Electron. Commun.59 (2005) 101. genRefLink(16, ’S0218271816400162BIB122’, ’10.1016
[123] 123. C. M. Krowne, IEEE Trans. Antennas Propag.32 (1984) 1224. genRefLink(16, ’S0218271816400162BIB123’, ’10.1109
[124] 124. C.M. Krowne, IEEE Trans. Magn.31 (1995) 2209, 4312. genRefLink(16, ’S0218271816400162BIB124’, ’10.1109
[125] 125. C. Altman and K. Suchy, Reciprocity, Spatial Mapping and Time Reversal in Electromagnetics, 2nd edn. (Springer Science+Business Media, Berlin, 2011). genRefLink(16, ’S0218271816400162BIB125’, ’10.1007 · Zbl 1235.78001
[126] 126. J. C. Monzon, Trans. Microwave Theory Technol.44 (1996) 10. genRefLink(16, ’S0218271816400162BIB126’, ’10.1109
[127] 127. J. C. Monzon, IEEE Trans. Microwave Theory Technol.44 (1996) 2299. genRefLink(16, ’S0218271816400162BIB127’, ’10.1109
[128] 128. M. Born and E. Wolf, Principles of Optics, 7th edn. (Cambridge University Press, Cambridge, UK, 1999). genRefLink(16, ’S0218271816400162BIB128’, ’10.1017
[129] 129. J. Hadamard, Lessons on the Propagation of Waves and the Equations of Hydrodynamics (Birkhäuser, Basel, 2011).
[130] 130. Y. N. Obukhov, T. Fukui and G. F. Rubilar, Phys. Rev. D62 (2000) 044050. genRefLink(16, ’S0218271816400162BIB130’, ’10.1103
[131] 131. F. W. Hehl, Y. N. Obukhov and G. F. Rubilar, Int. J. Mod. Phys. A17 (2002) 2695. [Abstract] genRefLink(128, ’S0218271816400162BIB131’, ’000177370900011’); genRefLink(64, ’S0218271816400162BIB131’, ’2002IJMPA..17.2695H’);
[132] 132. G. F. Rubilar, Ann. Phys. (Berlin)11 (2002) 717. genRefLink(16, ’S0218271816400162BIB132’, ’10.1002
[133] 133. Y. N. Obukhov and G. F. Rubilar, Phys. Rev. D66 (2002) 024042. genRefLink(16, ’S0218271816400162BIB133’, ’10.1103
[134] 134. F. P. Schuller, C. Witte and M. N. R. Wohlfarth, Ann. Phys. (NY)325 (2010) 1853. genRefLink(16, ’S0218271816400162BIB134’, ’10.1016
[135] 135. M. F. Dahl, Int. J. Geom. Methods Mod. Phys.9 (2012) 1250046. [Abstract] genRefLink(128, ’S0218271816400162BIB135’, ’000306075800012’);
[136] 136. P. M. Ho and T. Inami, Prog. Theor. Exp. Phys.2016 (2016) 013B03. genRefLink(16, ’S0218271816400162BIB136’, ’10.1093
[137] 137. Y. Itin, J. Phys. A42 (2009) 475402. genRefLink(16, ’S0218271816400162BIB137’, ’10.1088
[138] 138. E. E. Kummer, Über die Flächen vierten Grades mit sechzehn singulären Punkten (On surfaces of fourth order with sixteen singular points), (1864), In Ernst Eduard Kummer, Collected Papers (Springer, Berlin, 1975), pp. 418-432.
[139] 139. R. W. H. T. Hudson, Kummer’s Quartic Surface (Cambridge University Press, Cambridge, UK, 1903). · Zbl 0716.14025
[140] 140. P. Griffith and J. Harris, Principles of Algebraic Geometry (Wiley, New York, 1978).
[141] 141. P. Baekler, A. Favaro, Y. Itin and F. W. Hehl, Ann. Phys. (NY)349 (2014) 297. genRefLink(16, ’S0218271816400162BIB141’, ’10.1016
[142] 142. J. D. Zund, Ann. di Matem. Pura et Appl.110 (1976) 29. genRefLink(16, ’S0218271816400162BIB142’, ’10.1007
[143] 143. J. D. Zund, Ann. di Matem. Pura et Appl.82 (1969) 381. genRefLink(16, ’S0218271816400162BIB143’, ’10.1007
[144] 144. P. A. R. Ade et al., Phys. Rev. D92 (2015) 123509. genRefLink(16, ’S0218271816400162BIB144’, ’10.1103
[145] 145. H.-H. Mei et al., Astrophys. J.805 (2015) 107. genRefLink(16, ’S0218271816400162BIB145’, ’10.1088
[146] 146. W.-T. Ni, Phys. Lett. A379 (2015) 1297. genRefLink(16, ’S0218271816400162BIB146’, ’10.1016
[147] 147. W.-T. Ni, Int. J. Mod. Phys. Conf. Ser.40 (2016) 1660010. [Abstract] genRefLink(64, ’S0218271816400162BIB147’, ’2016IJMPS..4060010N’);
[148] 148. F. W. Hehl, Fundam. Theor. Phys.183 (2016) 77; this paper is reprinted in the present issue of IJMPD.
[149] 149. F. W. Hehl and Y. N. Obukhov, Found. Phys.35 (2004) 2007. genRefLink(16, ’S0218271816400162BIB149’, ’10.1007
[150] 150. C. Lämmerzahl and F. W. Hehl, Phys. Rev. D70 (2004) 105022. genRefLink(16, ’S0218271816400162BIB150’, ’10.1103
[151] 151. F. W. Hehl and Y. N. Obukhov, Lect. Notes Phys.702 (2006) 163. genRefLink(16, ’S0218271816400162BIB151’, ’10.1007
[152] 152. M. F. Dahl, J. Phys. A, Math. Theor.45 (2012) 405203. genRefLink(16, ’S0218271816400162BIB152’, ’10.1088
[153] 153. A. Favaro and L. Bergamin, Ann. Phys. (Berlin)523 (2011) 383. genRefLink(16, ’S0218271816400162BIB153’, ’10.1002
[154] 154. Y. Itin, Phys. Rev. D72 (2005) 087502. genRefLink(16, ’S0218271816400162BIB154’, ’10.1103
[155] 155. Y. Itin and Y. Friedman, Ann. Phys. (Berlin)17 (2008) 769. genRefLink(16, ’S0218271816400162BIB155’, ’10.1002
[156] 156. Y. Itin and F. W. Hehl, Ann. Phys. (NY)312 (2004) 60. genRefLink(16, ’S0218271816400162BIB156’, ’10.1016
[157] 157. W.-T. Ni, Phys. Lett. A378 (2014) 3413. genRefLink(16, ’S0218271816400162BIB157’, ’10.1016
[158] 158. F. Gronwald and F. W. Hehl, Stress and hyperstress as fundamental concepts in continuum mechanics and in relativistic field theory, in Advances in Modern Continuum Dynamics (Pitagora Editrice, Bologna, 1993), pp. 1-32; arXiv:gr-qc/9701054 [arXiv] .
[159] 159. F. W. Hehl, Y. N. Obukhov, G. F. Rubilar and M. Blagojevic, Phys. Lett. A347 (2005) 14. genRefLink(16, ’S0218271816400162BIB159’, ’10.1016
[160] 160. W.-T. Ni, Phys. Lett. A378 (2014) 1217. genRefLink(16, ’S0218271816400162BIB160’, ’10.1016
[161] 161. G. Ferrarese (ed.), Advances in Modern Continuum Dynamics, Int. Conf. Memory of A. Signorini, Isola d’Elba, June 1991 (Pitagora Editrice, Bologna, 1993).
[162] 162. O. Heaviside, Electromagnetic Theory, Vols. 1-3 (Benn, London, 1893, 1899, 1912). · JFM 30.0801.03
[163] 163. M. Kuhlmann and W. Pietsch, J. Gen. Philos. Sci.43 (2012) 209. genRefLink(16, ’S0218271816400162BIB163’, ’10.1007
[164] 164. J. Stark (ed.), Jahrbuch der Radioaktivität und Elektronik, Vol. 4 (1907) (Hirzel, Leipzig, 1908).
[165] 165. I. E. Tamm, Collected Papers, Vol. 1 (Nauka, Moscow, 1975) (in Russian).
[166] 166. J. Wallot, Dimensionen, Einheiten, Maßsysteme, in Handbuch der Physik, eds. H. Geiger and K. Scheel, Vol. II (Springer, Berlin, 1926), pp. 1-41; J. Wallot, Phys. Zeitschr.44 (1943) 17.
[167] 167. A. Weil (ed.), Ernst Eduard Kummer, Collected Papers, Vol. 2, Function Theory, Geometry and Miscellaneous, Vol. 2 (Springer, Berlin, 1975).
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.