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The historical developments of conformal transformations and symmetries are sketched: Their origin from stereographic projections of the globe, their blossoming in two dimensions within the field of analytic complex functions, the generic role of transformations by reciprocal radii in dimensions higher than two and their linearization in terms of polyspherical coordinates by Darboux, Weyl's attempt to extend General Relativity, the slow rise of finite dimensional conformal transformations in classical field theories and the problem of their interpretation, then since about 1970 the rapid spread of their acceptance for asymptotic and structural problems in quantum field theories and beyond, up to the current AdS/CFT conjecture.
An excellent survey on the history of synthetic geometry is E. Kötter, Die Entwicklung der synthetischen Geometrie von Monge bis auf Staudt (1847); Jahresber. d. Deutschen Mathematiker-Vereinig. 5
1901
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G. Darboux, Sur les transformations conformes de l’espace à trois dimensions; Archiv Mathematik u. Physik (3. Reihe) 1
1901
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C.F. Gauss, Disquisitiones generales circa superficies curvas, Werke 4
1902
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S. Haller, Beitrag zur Geschichte der konstruktiven Auflösung sphärischer Dreiecke durch stereographische Projektion; Bibliotheca Mathematica (Neue Folge) 13
1905
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V. Kommerell, Analytische Geometrie der Ebene und des Raumes, Chap. XXIV in: Vorlesungen über Geschichte der Mathematik, herausgeg. von M. Cantor, Bd. IV
1908
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H. Bateman, The transformation of the electrodynamical equations; Proc. London Math. Soc. (Ser. 2) 8
1909
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H. Minkowski, Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern; Nachr. Königl. Ges. Wiss. Göttingen, Math.- physik. Kl. 1908
1910
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H. Bateman, The transformations of coordinates which can be used to transform one physical problem into another; Proc. London Math. Soc. (Ser. 2) 8
1910
Earlier work this paper cites.
As to the life and work of William Thomson see: S.P. Thompson, The Life of William Thomson, Baron Kelvin of Largs, in two volumes (Macmillan and Co., London, 1910) here vol. I, Chap. III. Biography available under http://www.questia.com/PM.qst
1910
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H.R. Hassé, The equations of the theory of electrons transformed relative to a system in accelerated motion; Proc. London Math. Soc. (Ser. 2) 12
1913
Earlier work this paper cites.
(Lord) Rayleigh, The principle of similitude; Nature 95
1915
Earlier work this paper cites.
An impressive but quite subjective summary of the historical developments is given in the classical textbook by Felix Klein: F. Klein, Vorlesungen über höhere Geometrie, 3. Aufl., bearb. und hrsg. von W. Blaschke (Die Grundlehren der mathematischen Wissenschaften 22
1916
Earlier work this paper cites.
F. Engel, Über die zehn allgemeinen Integrale der klassischen Mechanik; Nachr. Königl. Gesellsch. Göttingen, Math. Physik. Klasse 1916
1916
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F. Engel, Nochmals die allgemeinen Integrale der klassischen Mechanik; Nachr. Königl. Gesellsch. Göttingen, Math. Physik. Klasse 1917
1917
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H. Bateman, The conformal transformations of a space of four dimensions and their applications to geometrical optics; Proc. London Math. Soc. (Ser. 2) 7
1918
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H. Weyl, Reine Infinitesimalgeometrie; Mathem. Zeitschr. 2
1918
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M. Bôcher, Ueber die Reihenentwicklungen der Potentialtheorie, mit einem Vorwort von Felix Klein (B.G. Teubner, Leipzig, 1894). As to M. Bôcher see G.D. Birkhoff, The scientific work of Maxime Bôcher; Bull. Amer. Math. Soc. 25
1919
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H. Weyl, Gravitation und Elektrizität; Sitzungsber. Königl. Preuß. Akad. Wiss. Berlin 1918
1921
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T. Kaluza, Zum Unitätsproblem der Physik; Sitzungsber. Königl. Preuß. Akad. Wiss. Berlin 1921
1921
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A. Einstein, Über eine naheliegende Ergänzung des Fundamentes der allgemeinen Relativitätstheorie; Sitzungsber. Königl. Preuß. Akad. Wiss. Berlin 1921
1921
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E. Bessel-Hagen, Über die Erhaltungssätze der Elektrodynamik; Mathem. Ann. 84
1921
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E. Schrödinger, Über eine bemerkenswerte Eigenschaft der Quantenbahnen eines einzelnen Elektrons; Zeitschr. Physik 12
1922
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H. Weyl, Space - Time - Matter, translation of the 4th German edition from 1921 by H.L. Brose (Methuen, London, 1922); the latest German edition is: Raum, Zeit, Materie: Vorlesungen über allgemeine Relativitätstheorie, 7. Aufl., hrsg. von J. Ehlers (Heidelberger Taschenbücher 251
1923
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S. Lie, Untersuchungen über Transformationsgruppen. II; Archiv f. Mathematik og Naturvidenskab 10
1924
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J.B. Durrande [called “feu”, i.e. deceased], Solution de deux des quatre problèmes de géometrie proposés à la page 68 du XI. e
1925
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Indeed, in 1860 Carl Gottfried Neumann (1832-1925) (the one from the boundary conditions) rediscovered the usefulness of the inversion for solving problems in potential theory: C. Neumann, Geometrische Methode, um das Potential der, von einer Kugel auf innere oder äussere Punkte ausgeübten, Wirkung zu bestimmen; Annalen der Physik und Chemie (2. Folge) 109
1925
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F. London, Quantenmechanische Deutung der Theorie von Weyl; Zeitschr. Physik 42
1927
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F. Bützberger, Über Bizentrische Polynome, Steinersche Kreis- und Kugelreihen und die Erfindung der Inversion (B.G. Teubner, Leipzig, 1913); I was not able to see this rare book, but learnt about its content from the summary by A. Emch, The discovery of inversion; Bull. Amer. Math. Soc. 20
1929
Earlier work this paper cites.
H. Weyl, Elektron und Gravitation. I.; Zeitschr. Physik 56
1929
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Jakob Steiner, Allgemeine Theorie über das Berühren und Schneiden der Kreise und der Kugeln, hrsg. von R. Fueter and F. Gonseth (Veröff. Schweiz. Mathem. Gesellschaft 5
1931
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H. Weyl, Geometrie und Physik; Die Naturwiss. 19
1931
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E. Schrödinger, Diracsches Elektron im Schwerefeld I; Sitz.-Ber. Preuss. Akad. Wiss., Physik.-Mathem. Klasse, 1932
1932
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B.C. Patterson, The origins of the geometric principle of inversion, Isis 19
1933
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Quite helpful and informative for the subject of the present paper are also several articles in the Encyklopädie der Mathematischen Wissenschaften, mit Einschluss ihrer Anwendungen, III. Band in 3 Teilen: Geometrie, redig. von W.Fr. Meyer u. H. Mohrmann (B.G. Teubner, Leipzig, 1907-1934); Bd. III, 1. Teil, 1. Hälfte: article 4b. by G. Fano, article 7. by E. Müller; Bd. III, 1. Teil, 2. Hälfte: article 9. by M. Zacharias; Bd. III, 2. Teil, 2. Hälfte. B.: article 11. by L. Berzolari; Bd. III, 3. Teil: article 6. by A. Voss, article 7. by H. Liebmann, article 9. by E. Salkowski. All volumes are available from GDZ: http://gdz.sub.uni-goettingen.de/
1934
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S. Lie, Ueber diejenige Theorie eines Raumes mit beliebig vielen Dimensionen, die der Krümmungs-Theorie des gewöhnlichen Raumes entspricht; Nachr. Königl. Gesellsch. Wiss. u. d. G. - A. - Univ. Göttingen 1871
1934
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J.A. Schouten and J. Haantjes, Über die konforminvariante Gestalt der Maxwellschen Gleichungen und der elektromagnetischen Impuls-Energiegleichungen; Physica 1
1934
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P.A.M. Dirac, Wave equation in conformal space; Ann. Math. 37
1935
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R. Brauer and H. Weyl, Spinors in n n dimensions; Amer. Journ. Math. 57
1935
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O. Veblen, A conformal wave equation; Proc. Nat. Acad. Sci. USA 21
1935
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E.A. Milne, Relativity, Gravitation and World-Structure (At the Clarendon Press, Oxford, 1935)
1935
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H.J. Bhabha, The wave equation in conformal space; Proc. Cambridge Philos. Soc. 32
1936
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In 1951 Segal discussed the transition of the conformal group O ( 2 , 4 ) O(2,4) to the Poincaré group by contracting the bilinear Casimir operator of the former to that of the latter: I.E. Segal, A class of operator algebras which are determined by groups; Duke Math. Journ. 18
1936
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J.A. Schouten and Haantjes, Über die konforminvariante Gestalt der relativistischen Bewegungsgleichungen; Koningl. Akad. Wetensch. Amsterdam, Proc. Sect. Sci. 39
1936
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L. Page, A new relativity; paper I. Fundamental principles and transformations between accelerated systems; Phys. Rev. 49
1936
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H.P. Robertson, An interpretation of Page’s “New Relativity”; Phys. Rev. 49
1936
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H.P. Robertson, Kinematics and World-Structure, parts I-III; Astrophys. Journ. 82
1936
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H.T. Engstrom and M. Zorn, The transformation of reference systems in the Page relativity; Phys. Rev. 49
1936
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S. Lie, Ueber Complexe, insbesondere Linien- und Kugel-Complexe, mit Anwendung auf die Theorie partieller Differentialgleichungen; Mathem. Annalen 5
1937
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J. Levine, Groups of motions in conformally flat spaces; Bull. Amer. Math. Soc. 42
1939
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J. Haantjes, Die Gleichberechtigung gleichförmig beschleunigter Beobachter für die elektromagnetischen Erscheinungen; Koningl. Akad. Wetensch. Amsterdam, Proc. Sect. Sci. 43
1940
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W. Pauli, Über die Invarianz der Dirac’schen Wellengleichungen gegenüber Ähnlichkeitstransformationen des Linienelementes im Fall verschwindender Ruhemasse; Helv. Phys. Acta 13
1940
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A. Wintner, The Analytical Foundations of Celestial Mechanics (Princeton Univ. Press, Princeton NJ, 1941) here §155 - §162, especially Eqs. (16) and (16 bis) of Chap. III
1941
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J. Haantjes, The conformal Dirac equation; Koningl. Akad. Wetensch. Amsterdam, Proc. Sect. Sci. 44
1941
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J.A. McLennan Jr., Conformal invariance and conservation laws for relativistic wave equations for zero rest mass; Il Nuovo Cim. (Ser. 10) 3
1945
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L. Infeld, A new approach to relativistic cosmology; Nature 156
1946
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N.H. Kuiper, On conformally-flat spaces in the large; Ann. Math. 50
1949
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E.L. Hill, On accelerated coordinate systems in classical and relativistic mechanics; Phys. Rev. 67
1951
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H. Minkowski, Raum und Zeit; Physikal. Zeitschr. 10
1952
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A.F. Möbius, Ueber eine neue Verwandtschaft zwischen ebenen Figuren; originally published in 1853, reprinted in: August Ferdinand Möbius, Gesammelte Werke 2
1952
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H. Poincaré, Sur le problème des trois corps et les équations de la dynamique; Acta Mathem. 13
1952
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J.A. Schouten, Ricci-Calculus, 2nd Ed. (Die Grundlehren der Mathem. Wiss. in Einzeldarst. 10
1954
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L. Euler, De representatione superficiei sphericae super plano [1]. De proiectione geographica superficiei [2]. De proiectione geographica de Lisliana in mappa generali imperii russici usitata [3]. The papers are published in: L. Euler, Opera Omnia, Ser. I, 28
1955
Cited alongside, same era.
F. Gürsey, On a conform-invariant spinor wave equation; Il Nuovo Cim. (Ser. 10) 3
1956
Cited alongside, same era.
S.A. Bludman, Some theoretical consequences of a particle having mass zero; Phys. Rev. 107
1957
Cited alongside, same era.
W. Heisenberg, Zur Quantisierung nichtlinearer Gleichungen; Nachr. Akad. Wiss. Göttingen, Math.- Physik. Klasse, Jahrg. 1953
1957
Cited alongside, same era.
J.A. McLennan, Jr., Conformally invariant wave equations for non-linear and interacting fields; Il Nuovo Cim. (Ser. 10) 5
1957
Cited alongside, same era.
Trends in Elementary Particle Theory, Intern. Summer Inst. Theor. Physics Bonn 1974, ed. by H. Rollnik and K. Dietz (Lecture Notes in Physics 37
1975
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T.H. Go, Some remarks on conformal invariant theories on four-Lorentz manifolds; Comm. math. Phys. 41
1975
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R. Haag, J.T. Łopuszański and M. Sohnius, All possible generators of supersymmetries of the S S -matrix; Nucl. Phys. B 88
1975
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More on scale and conformal symmetries in non-relativistic and relativistic systems is contained in the (unpublished but available) notes of my guest lectures given during the summer term 1971 at the University of Hamburg and at DESY. See also V. de Alfaro, S. Fubini and G. Furlan, Conformal invariance in quantum mechanics; Il Nuovo Cim. (Ser. 11) 34 A
1976
Later among the works it cites.
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A.S. Wightman, Relativistic invariance and quantum mechanics (notes by A. Barut); Suppl. Nuovo Cim. (Ser. 10) 14
1959
Cited alongside, same era.
H.-P. Dürr, W. Heisenberg, H. Mitter, S. Schlieder und K. Yamazaki, Zur Theorie der Elementarteilchen; Zeitschr. Naturf. 14 a
1959
Cited alongside, same era.
F. Bopp and F.L. Bauer, Feldmechanische Wellengleichungen für Elementarteilchen verschiedenen Spins; Zeitschr. Naturf. 4 a
1959
Cited alongside, same era.
J. Wess, On scale transformations; Il Nuovo Cim. (Ser. 10) 14
1959
Cited alongside, same era.
L.D. Landau and E.M. Lifshitz, Mechanics (Vol. 1 of Course of Theoretical Physics
1960
Cited alongside, same era.
R.L. Ingraham, Conformal relativity; Proc. Nat. Acad. Sci. USA 38
1960
Cited alongside, same era.
J. Wess, The conformal invariance in quantum field theory; Il Nuovo Cim. (Ser. 10) 18
1960
Cited alongside, same era.
1976
Later among the works it cites.
B. Schroer, A necessary and sufficient condition for the softness of the trace of the energy-momentum tensor; Lett. Nuovo Cim. (Ser. 2) 2
1977
Later among the works it cites.
M. Lüscher and G. Mack, Global conformal invariance in quantum field theory; Comm. math. Phys. 41
1977
Later among the works it cites.
I mention only some of the later papers, from which earlier ones may be traced back: W. Rühl, Distributions on Minkowski space and their connection with analytic representations of the conformal group; Comm. math. Phys. 27
1977
Later among the works it cites.
E. Cunningham, The principle of relativity in electrodynamics and an extension thereof; Proc. London Math. Soc. (Ser. 2) 8
1978
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Jordanus de Nemore and the Mathematics of Astrolabes: De Plana Spera
1978
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I.T. Todorov, M.C. Mintchev and V.B. Petkova, Conformal Invariance in Quantum Field Theory (Scuola Normale Superiore Pisa, Classe di Scienze
1978
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See, e.g. L.V. Ahlfors, Complex Analysis, An Introduction to the Theory of Analytic Functions of One Complex Variable, 3rd Ed. (McGraw-Hill Book Co., New York etc., 1979) here Chap. 6 with the details of assumptions and proof
1979
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C. Itzykson and J.-B. Zuber, Quantum Fiel Theory (Intern. Series in Pure and Appl. Physics, McGraw-Hill, Inc., New York etc., 1980) here Chap. 13
1980
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O. Neugebauer, The early history of the astrolabe; Isis 40
1981
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Results of those rediscoveries of Harriot’s work are summarized in Thomas Harriot, Renaissance Scientist, ed. by J. Shirley (Clarendon Press, Oxford, 1974) where J.V. Pepper’s contribution (Harriot’s earlier work on mathematical navigation: theory and praxis) on pp. 54-90 is of special interest. J.W. Shirley, Thomas Harriot: A Biography (Clarendon Press, Oxford, 1983)
1983
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Francisci Aguilonii, e Societate Iesu, Opticorum Libri Sex, Philosophis iuxta ac Mathematicis utiles (Ex Officina Plantiniana, Apud Viduam et Filios Io. Moreti, Antwerpiae, 1613) [From Franciscus Aguilonius, Six Books on Optics, equally useful for Philosophers and Mathematicians]; as to François d’Aiguillon (or de Aguilón) see A. Ziggelaar S. J., François de Aguilón, S. J. (1567-1617), Scientist and Architect (Bibliotheca Instituti Historici S. I. 44
1983
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L. Euler, Considerationes de traiectoriis orthogonalibus, Opera Omnia, Ref. [ 28 ] , pp. 99-119. German translation in: Zur Theorie Komplexer Funktionen, Arbeiten von Leonhard Euler, eingeleitet und mit Anmerkungen versehen von A.P. Juschkewitsch (Ostwalds Klassiker der Exakten Wissenschaften 261
1983
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R.M. Wald, General Relativity (The University of Chicago Press, Chicago and London,1984) here Appendix D
1984
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A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theory; Nucl. Phys. B 24
1984
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S. Coleman, Dilatations; in: Properties of the Fundamental Interactions, part A, 1971 Intern. School Subnuclear Physics, Erice, Trapani-Sicily, July 8-26, 1971, ed. by A. Zichichi (The subnuclear series 9
1985
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M.F. Sohnius, Introducing supersymmetry; Phys. Rep. 128
1985
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M.A. Virasoro, Subsidiary conditions and ghosts in dual-resonance models; Phys. Rev. D 1
1986
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The history of conservation laws before and after E. Noether’s seminal paper has been discussed in the following conference contribution: H.A. Kastrup, The contributions of Emmy Noether, Felix Klein and Sophus Lie to the modern concept of symmetries in physical systems; in: Symmetries in Physics (1600-1980), 1st Intern. Meeting on the History of Scient. Ideas, Sant Feliu de Guíxols, Catalonia, Spain, Sept. 20-26, 1983, ed. by M.G. Doncel, A. Hermann, L. Michel and A. Pais (Seminari d’Història de les Ciències, Universitat Autònoma de Barcelona, Bellaterra (Barcelona) Spain, 1987) here pp. 113-163
1987
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M.B. Green, J.H. Schwarz and E. Witten, Superstring Theory I (Cambridge Univ. Press, Cambridge etc., 1987) here Chap. 3
1987
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G. Mack, Introduction to conformal invariant quantum field theory in two or more dimensions; in: Nonperturbative Quantum Field Theory, Proc. NATO Advanced Study Institute, Cargèse, July 16-30, 1987, ed. by G. ’t Hooft, A. Jaffe, G. Mack, P.K. Mitter and R. Stora (NATO ASI Series B 185
1988
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J. Polchinski, Scale and conformal invariance in quantum field theory; Nucl. Phys. B 303
1988
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Conformal Invariance and Applications to Statistical Mechanics, Reprints ed. by C. Itzykson, H. Saleur and J.-B. Zuber (World Scientific, Singapore etc., 1988)
1988
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B. Riemann, Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse, in: Bernhard Riemann, Collected Papers, newly ed. by R. Narasimhan (Springer-Verlag, Berlin etc.; B.G. Teubner Verlagsgesellschaft, Leipzig, 1990) pp. 35-80 (pp. 3-48 in the edition from 1892); older edition available from UMDL: http://quod.lib.umich.edu/u/umhistmath/
1990
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Contributions by J.L. Cardy (Conformal invariance and statistical mechanics) and P. Ginsparg (Applied conformal field theory) in: Fields, Strings and Critical Phenomena, Les Houches Summer School on Theoretical Physics, Sess. 49, June 28 - Aug. 5, 1988, ed. by E. Brezin and J. Zinn-Justin (North-Holland, Amsterdam etc., 1990)
1990
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P.C. West, Introduction to Supersymmetry and Supergravity, extend. 2nd ed. (World Scient. Publ., Singapore etc., 1990)
1990
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See , e.g. as one of many possible examples: R. Schinzinger and P.A.A. Laura, Conformal Mapping: Methods and Applications (Elsevier Science Publishers B.V., Amsterdam etc., 1991)
1991
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J. Wess and J. Bagger, Supersymmetry and Supergravity, 2. ed., rev. and expand. (Princeton Univ. Press, Princeton NJ, 1992)
1992
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As to the early history of map projections see, e.g. J. Keuning, The history of geographical map projections until 1600; Imago Mundi 12
1993
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P. Christe and M. Henkel, Introduction to Conformal Invariance and Its Applications to Critical Phenomena (Lecture Notes in Physics m 16
1993
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C. Ptolemaeus, Planisphaerium, in: Claudii Ptolemaei Opera Quae Exstant Omnia, vol. II (Opera Astronomica Minora), ed. by J.L. Heiberg (B.G. Teubner, Leipzig, 1907) pp. 222-259; German translation by J. Drecker, Isis 9
1994
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This remark does not apply to J. Wess and W. Thirring who already in 1962 invited me to Vienna for a seminar on the subject of my Ph.D. Thesis. But otherwise: Once, when I was about to receive my Ph.D. 1962 in Munich, I was offered an Assistent position under the condition that I quit my work on the conformal group (I refused). The acceptance was similar reserved during my years in Berkeley (1964/65) and Princeton (1965/66): When in 1966 – at a Midwest Conference on Theoretical Physics in Bloomington – Sidney Coleman heard me talk to Rudolf Haag about my interest in the conformal group, he commented: “I shall never work on this!” A few years later he wrote several papers on the subject! Also, later Arthur Wightman told me that he and his colleagues in Princeton did not appreciate the possible importance of the conformal group when I was there. I was very grateful to Eugene Wigner (1902-1995) for his invitation to come to Princeton in order to work on scale and conformal invariance, but he was not much interested in asymptotic symmetries at very high energies and wanted the continuous 2-particle energy spectrum to be analysed in the framework of scale invariance etc. This was then done in the Ph.D. thesis of A.H. Clark, Jr.: The Representation of the Special Conformal Group in High Energy Physics; Princeton University, Department of Physics, 1968
1995
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S.V. Ketov, Conformal Field Theory (World Scientific, Singapore etc., 1995); mainly on 2-dimensional theories
1995
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S. Weinberg, The Quantum Theory of Fields, vol. II: Modern Applications (Cambridge Univ. Press, Cambridge, 1996) here especially Chaps. 18 and 20
1996
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J. Cardy, Scaling and Renormalization in Statistical Physics (Cambridge Lecture Notes in Physics 5
1996
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L. O’Raifeartaigh, The Dawning of Gauge Theory (Princeton Series in Physics, Princeton University Press, Princeton NJ, 1997); contains edited reprints and translations of important papers in the development of gauge theories
1997
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J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, 3rd ed. (Clarendon Press, Oxford, 1997) here especially Chap. 10
1997
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Letter of Weyl to Einstein, The Collected Papers of Albert Einstein (abbr. CPAE in the following), ed. R. Schulmann et al., vol. 8 B
1998
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E.S. Fradkin and M.Ya. Palchik, Conformal Quantum Field Theory in D-dimensions (Mathematics and Its Applications; Kluwer Academic Publishers, Dordrecht etc., 1996); New developments in D D -dimensional conformal quantum field theory; Phys. Rep. 300
1998
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J.M. Maldacena, The large N N limit of superconformal field theories and supergravity; Adv. Theor. Math. Phys. 2
1998
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E. Witten, Anti de Sitter space and holography; Adv. Theor. Math. Phys. 2
1998
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L. O’Raifeartaigh and N. Straumann, Gauge theory: Historical origins and some modern developments; Rev. Mod. Phys. 72
2000
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W. Nahm, Conformal field theory: a bridge over troubled waters; in: Quantum Field Theory, A Twentieth Century Profile, with a Foreword by Freeman J. Dyson, ed. by A.N. Mitra (Hindustan Book Agency and Indian National Science Academy, Dehli, 2000) here Chap. 22, pp. 571-604
2000
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J. Polchinski, String Theory I (An Introduction to the Bosonic String) and II (Superstring Theory and Beyond) (Cambridge Univ. Press, Cambridge etc., 2000) here especially I, Chap. 2, and II, Chap. 15
2000
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S. Weinberg, The Quantum Theory of Fields, vol. III: Supersymmetry (Cambridge Univ. Press, Cambridge etc., 2000)
2000
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Hermann Weyl’s Raum - Zeit - Materie
2001
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P.C. West, A review of non-renormalization theorems in supersymmetric theories; Nucl. Phys. B (Proc. Suppl.) 101
2001
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As to the prehistory (d’Alembert, Euler, Laplace) and Cauchy’s part in formulating the conditions see B. Belhoste, Augustin-Louis Cauchy, A Biography (Springer-Verlag, New York etc., 1991); F. Smithies, Cauchy and the Creation of Complex Function Theory (Cambridge University Press, Cambridge UK, 1997). As to the relations between Cauchy and Gauss see K. Reich, Cauchy and Gauß. Cauchys Rezeption im Umfeld von Gauß; Arch. Hist. Exact Sci. 57
2003
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As to Mercator see A. Taylor, The World of Gerhard Mercator, The Mapmaker Who Revolutionised Geography (Harper Perennial, London etc., 2004). M. Monmonier, Rhumb Lines and Map Wars, A Social History of the Mercator Projection (The University of Chicago Press, Chicago and London, 2004)
2004
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H.F.M. Goenner, On the History of Unified Field Theories; Living Reviews, http://www.livingreviews.org/lrr-2004-2
2004
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J. Frauendiener, Conformal Infinity; Living Reviews, http://www.livingreviews.org/lrr-2004-1
2004
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K. Gawȩdzki, Conformal field theory: a case study; in: New Non-Perturbative Methods in String and Field Theory, ed. by Y. Nutku, C. Saclioglu and T. Turgut (Frontiers in Physics 102
2004
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See Appendix 3 of the next Ref. [ 11 ] : “Al-Farghānī’s Proof of the Basic Theorem of Stereographic Projection” by N.D. Sergeyeva and L.M. Karpova, pp. 210-217; Al-Farghānī, On the Astrolabe, Arabic Text Edition with Translation and Commentary by R. Lorch (Boethius Texte u. Abhandl. Geschichte Mathem. u. Naturw. 52
2005
Later among the works it cites.
2005
Later among the works it cites.
K.-H. Rehren, Algebraic holography; Ann. Henri Poincaré 1
2005
Later among the works it cites.
F.T. Schubert, De proiectione sphaeroidis ellipticae geographica. Dissertatio prima. (presented on May 22, 1788), Nova Acta Academiae Scientiarum Imperialis Petropolitanae V
2007
Later among the works it cites.
H. Georgi, Unparticle Physics; Phys. Rev. Lett. 98
2008
Closest in time.