Skip to main content
SpringerLink
Log in

Historical Background

  • Chapter
  • First Online:
Geometrodynamics of Gauge Fields

Part of the book series: Mathematical Physics Studies ((MPST))

  • 1475 Accesses

Abstract

Despite a long history, the gauge-theoretic status of gravitation still remains the single gap in the quantum gauge picture of fundamental interactions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    “Alle Zweifel sind entschwunden, Endlich ist es nun gefunden: Das Licht, das läuft natürlich krumm Zu Einsteins allergrößtem Ruhm!” (Postcard sent to Einstein by Debye, Weyl, and others at October 11,1919).

  2. 2.

    Cf. (Mielke 1985).

  3. 3.

    “Es ist also sehr wohl denkbar, daß die Ma\(\ss \)verhältnisse des Raumes im Unendlichkleinen den Voraussetzungen der [Euklidischen] Geometrie nicht gemäßsind, und dies würde man in der Tat annehmen müssen, sobald sich dadurch die Erscheinungen auf einfachere Weise erklären lie\(\ss \)en.” (Riemann, Habilitations-Colloquium vom 10. Juni 1854, p 285).

  4. 4.

    Falls der Raum im Kleinen mehrfach zusammenhängend ist, kann man nicht mehr “sagen: hier ist Ladung, sondern nur: diese im Felde verlaufende geschlossene Fläche schließt Ladung ein.”.

  5. 5.

    Wheeler’s formulations have been adopted here for our purposes (1968, p 4).

References

  • Adler S (1980) Some Strangeness in the Proportion. In: Woolf H (ed) A Centennial Symposium to Celebrate the Achievements of Albert Einstein. Addison-Wesley, Reading, p 494

    Google Scholar 

  • Arnison G (1983) Experimental observation of isolated large transverse energy electrons with associated missing energy at \(\sqrt{\rm {s}}\) = 540 GeV. Phys Lett B 122:103–116

    Google Scholar 

  • Baekler P, Hehl FW, Mielke EW (1982) Vacuum solutions with double duality properties of a quadratic Poincaré gauge field theory. In: Ruffini R (ed) 2nd Marcel Grossmann Meeting on the Recent Progress of the Fundamental, of General Relativity (North Holland Publ., Amsterdam), p 413

    Google Scholar 

  • Bernstein H, Phillips AV (1981) Fiber bundles and quantum theory. Sci Am 245(1):122–137

    Google Scholar 

  • Bjorken JD, Drell SD (1964) Relativistic quantum mechanics. McGraw-Hill, San Francisco

    MATH  Google Scholar 

  • Chodos A, Jaffe RL, Johnson K, Thorn CB, Weisskopf VF (1974) New extended model of hadrons. Phys Rev D 9(12):3471

    Article  ADS  MathSciNet  Google Scholar 

  • Clifford WK (1982) On the space-theory of matter. In: Tucker R (ed) Mathematical Papers. Macmillan, London, p 21

    Google Scholar 

  • Dirac PAM (1928) The quantum theory of the electron. part I, II. In: Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences, vol A117–A118, pp 610, 351

    Google Scholar 

  • Eddington AS (1920) The Mathematical Theory of Relativity. Cambridge University Press, Cambridge

    Google Scholar 

  • Einstein A (1915) Zur allgemeinen Relativitätstheories. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (Berlin) 1:799–801

    MATH  Google Scholar 

  • Einstein A (1916) Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik 354(7):769–822

    Article  ADS  MATH  Google Scholar 

  • Einstein A (1950) The Bianchi identities in the generalized theory of gravitation. Can J Math 2:120–128

    Article  MathSciNet  MATH  Google Scholar 

  • Einstein A, Grossmann M (1913) Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation (I. Physikalischer Teil von A. Einstein. II. Mathematischer Teil von M. Grossmann). Zeitschr Math Phys 62, 225

    Google Scholar 

  • Einstein A, Mayer W (1931) Einheitliche Theorie von Gravitation und Elektrizität; 2. Preussische Akademie der Wissenschaften, Phys.-math. Klasse, Sitzungsberichte, 541557(1932):130137

    Google Scholar 

  • Einstein A, Rosen N (1935) The particle problem in the general theory of relativity. Phys Rev 48(1):73

    Article  ADS  MATH  Google Scholar 

  • Eötvös von R (1890) Über die Anziehung der Erde auf verschiedene Substanzen. Mathematische und Naturwissenschaftliche Berichte aus Ungarn 8:65–68

    Google Scholar 

  • Gell-Mann M, Ne’eman Y (1964) The eightfold way. Benjamin, New York

    Google Scholar 

  • Geroch RP (1966) Electromagnetism as an aspect of geometry?: already unified field theory. The null field case. Ann Phys 36(2):147–187

    Article  ADS  MathSciNet  Google Scholar 

  • Graves JC (1971) The conceptual foundations of contemporary relativity theory. M.I.T. Press, Cambridge

    Google Scholar 

  • Greenberg OW, Nelson CA (1977) Color models of hadrons. Phys Rep 32(2):69–121

    Article  ADS  Google Scholar 

  • Hehl F (1980) Four lectures on Poincaré gauge field theory. In: Bergmann PG, de Sabbata V (eds) Proceedings of the 6th course on spin, torsion, rotation, and supergravity, held at Erice, Italy, May 1979. Plenum, New York, pp 5–61

    Google Scholar 

  • Hehl F (1981) Zur Eichfeldtheorie der Gravitation. Grundlagenprobleme der modernen Physik, Nitsch, J., Pfarr, J. und Stachow, E.-W., Bibliographisches Institut Mannheim

    Google Scholar 

  • Hehl FW (1970) Spin und Torsion in der allgemeinen Relativitätstheorie. Universität Clausthal, Habilitationsschrift

    Google Scholar 

  • Hehl FW, Von der Heyde P, Kerlick GD, Nester JM (1976) General relativity with spin and torsion: foundations and prospects. Rev Mod Phys 48(3):393

    Article  ADS  MathSciNet  Google Scholar 

  • Heisenberg W (1967) Einführung in die einheitliche Feldtheorie der Elementarteilchen. Hirzel Stuttgart

    Google Scholar 

  • Hübner K (1983) Critique of scientific reason. Chicago University Press, Chicago

    Google Scholar 

  • Kaluza T (1921) Zum Unitätsproblem der Physik. Sitzungsber. Preuss. Akad. Wiss. Berlin. Math Phys 1921(966972):45

    Google Scholar 

  • Kanitscheider B (1971) Geometrie und Wirklichkeit, vol 36. Duncker & Humblot, Berlin, 389 p 1

    Google Scholar 

  • Kerr RP (1963) Gravitational field of a spinning mass as an example of algebraically special metrics. Phys Rev Lett 11(5):237

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Kibble T (1961) Lorentz invariance and the gravitational field. J Math Phys 2(2):212–221

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Kibble TWB (1967) Symmetry breaking in non-abelian gauge theories. Phys Rev 155(5):1554

    Article  ADS  Google Scholar 

  • Klein O (1926) Quantentheorie und fünfdimensionale Relativitätstheorie. Zeitschrift für Physik 37(12):895–906

    Article  ADS  MATH  Google Scholar 

  • Kobayashi S, Nomizu K (1963) Foundations of differential geometry, vol 1. Interscience Publishers, New York

    Google Scholar 

  • Kokkedee JJJ (1969) The Quark model. Benjamin, New York

    Google Scholar 

  • Kuchař K (1966) The Rainich geometrization of fermion fields, Acta Physica Polonia XXVIII, 695

    Google Scholar 

  • Landau LD, Lifshitz EM (1965) Quantum mechanics, Non-relaticistic Theory. Pergamon Press, New York

    Google Scholar 

  • London F (1927a) Die Theorie von Weyl und die Quantenmechanik. Naturwissenschaften 15(8):187–187

    Article  ADS  MATH  Google Scholar 

  • London F (1927b) Quantenmechanische Deutung der Theorie von Weyl. Zeitschrift für Physik A 42(5):375–389

    Google Scholar 

  • Marciano W, Pagels H (1978) Quantum chromodynamics. Phys Rep 36(3):137–276

    Article  ADS  Google Scholar 

  • Maxwell JC (1881) A treatise on electricity and magnetism, vol 1. Clarendon press, Oxford

    Google Scholar 

  • Mielke EW (1977) Outline of a new geometrodynamical model of extended baryons. Phys Rev Lett 39(9):530

    Article  ADS  MathSciNet  Google Scholar 

  • Mielke EW (1980) The eightfold way to color geometrodynamics. Int J Theor Phys 19(3):189–209

    Article  MathSciNet  Google Scholar 

  • Mielke EW (1981) Empirical verification of recently proposed hadron mass formulas. Zeitschrift für Naturforschung A 36(12):1315–1318

    Article  ADS  Google Scholar 

  • Mielke EW (1984a) Reduction of the Poincaré gauge field equations by means of duality rotations. J Math Phys 25(3):663–668

    Article  ADS  MathSciNet  Google Scholar 

  • Mielke EW (1984b) On pseudoparticle solutions in the Poincaré gauge theory of gravity. Fortschritte der Physik 32(12):639–660

    Article  ADS  MathSciNet  Google Scholar 

  • Mielke EW (1985) Bemerkungen zur Geometrisierung fundamentaler Wechselwirkungen der Physik. Naturwissenschaften 72(3):118–124

    Article  ADS  Google Scholar 

  • Misner C, Wheeler J (1957) Classical physics as geometry: Gravitation, electromagnetism, unquantized charge, and mass as properties of curved empty space. Ann Phys 2(1957):525–603

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Misner C, Thorne K, Wheeler J (1973) Gravitation. Freeman and Co, San Francisco (quoted as MTW)

    Google Scholar 

  • Nieuwenhuizen Van P (1981) Supergravity. Phys Rep 68(4):189–398

    Article  ADS  MathSciNet  Google Scholar 

  • Rainich GY (1925) Electrodynamics in the general relativity theory. Trans Am MathSoc 27(1):106–136

    Article  MathSciNet  MATH  Google Scholar 

  • Riemann B (1854) Ueber die Hypothesen, welche der Geometrie zu Grunde liegen. Bernhard Riemann’s Gesammelte Mathematische Werke, H. Weber, Hrsg., 2. Aufl. Dover Publcations, New York, p 272, 1953; English translation by W.K. Clifford, Nature 8, 14 (1873)

    Google Scholar 

  • Salam A (1968) Weak and electromagnetic interactions in Elementary Particle Theory. In: Svartholm N (ed) Stockholm (Amqvist & Wiksell, Stockholm), p 367

    Google Scholar 

  • Salam A (1973) On SL (6, \({\mathbb{C}} \)) gauge invariance, in Fundamental Interactions in Physics. Kursunoǧlu B et al. (eds) 1973 Coral Gables conference. Plenum, New York, p 55

    Google Scholar 

  • Salam A (1980) Gauge unification of fundamental forces. Rev Mod Phys 52(3):525

    Article  ADS  MathSciNet  Google Scholar 

  • Salam A, Strathdee J (1977a) A steeply-rising potential in tensor gauge theory. Phys Lett B 67(4):429–431

    Google Scholar 

  • Salam A, Strathdee J (1977b) Class of solutions for the strong-gravity equations. Phys Rev D 16(8):2668

    Google Scholar 

  • Salam A, Strathdee J (1978) Remarks on high-energy stability and renormalizability of gravity theory. Phys Rev D 18(12):4480

    Google Scholar 

  • Sciama DW (1962) On the analogy between charge and spin in general relativity. Recent developments in general relativity. Pergamon Press, Oxford, p 415

    Google Scholar 

  • Shaw R (1955) The problem of particle types and other contributions to the theory of elementary particles, Cambridge. Ph.D. thesis

    Google Scholar 

  • Taylor JC (1979) Gauge theories of weak interactions. Cambridge University Press, Cambridge

    Google Scholar 

  • Uhlenbeck GE, Goudsmit S (1925) Ersetzung der Hypothese vom unmechanischen Zwang durch eine Forderung bezüglich des inneren Verhaltens jedes einzelnen Elektrons. Naturwissenschaften 13(47):953–954

    Article  ADS  MATH  Google Scholar 

  • Utiyama R (1956) Invariant theoretical interpretation of interaction. Phys Rev 101(5):1597

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Weyl H (1918) Gravitation und Elektrizität. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (Berlin), Seite 465-478, 1:465–478

    Google Scholar 

  • Weyl H (1924) Was ist Materie? Naturwissenschaften 12(30):604–611

    Google Scholar 

  • Weyl H (1928) Gruppentheorie und Quantenmechanik S.Hirzel, Leipzig

    Google Scholar 

  • Weyl H (1929) Gravitation and the electron. Proc Nat Acad Sci 15(4):323–334

    Google Scholar 

  • Weyl H (1950) A remark on the coupling of gravitation and electron. Phys Rev 77:699

    Google Scholar 

  • Wheeler JA (1955) Geons. Phys Rev 97(2):511

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Wheeler JA (1962). Curved empty space as the building material of the physical world: an assessment. In: Nagel E, Suppes P, Tarski A (eds) Logic, methodology and philosophy of science. Proceedings of the 1960 international congress. Stanford University Press, pp 361–374

    Google Scholar 

  • Wheeler JA (1964a) Geometrodynamics and the issue of the final state. In: de Witt C, de Witt BS (eds) Relativity, groups, and topology. Gordon and Breach, New York, pp 315–520

    Google Scholar 

  • Wheeler JA (1964b) Mach’s principle as boundary condition for Einstein’s field equations and as a central part of the “plan” of general relativity. In: Proceedings theory of gravitation, Gauthier-Villars, Paris, PWN-Polish Scientific Publishers, Warszawa

    Google Scholar 

  • Wheeler JA (1968) Superspace and the nature of quantum geometrodynamics. In: Zabusky Norman J (ed) Topics in Nonlinear Physics. Springer, New York, pp 615–724

    Google Scholar 

  • Wheeler JA (1974) The black hole. In: Proceedings of the sixteenth Solvay conference (Editions de l’Université de Bruxelles, Brussels), p 279

    Google Scholar 

  • Will CM (1993) Theory and experiment in gravitational physics. Cambridge University Press, Cambridge

    Google Scholar 

  • Wilson KG (1974) Confinement of quarks. Phys Rev D 10(8):2445

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Física, CBI Iztapalapa, Universidad Autónoma Metropolitana, Mexico City, México

    Eckehard W. Mielke

Authors
  1. Eckehard W. Mielke
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eckehard W. Mielke .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Mielke, E.W. (2017). Historical Background. In: Geometrodynamics of Gauge Fields. Mathematical Physics Studies. Springer, Cham. https://doi.org/10.1007/978-3-319-29734-7_1

Download citation

Publish with us

Policies and ethics

Search

Navigation