"On the History of Unified Field Theories. Part II. (ca. 1930 – ca. 1965)"
Hubert F. M. Goenner 
1 Introduction
2 Mathematical Preliminaries
2.1 Metrical structure
2.2 Symmetries
2.3 Affine geometry
2.4 Differential forms
2.5 Classification of geometries
2.6 Number fields
3 Interlude: Meanderings – UFT in the late 1930s and the 1940s
3.1 Projective and conformal relativity theory
3.2 Continued studies of Kaluza–Klein theory in Princeton, and elsewhere
3.3 Non-local fields
4 Unified Field Theory and Quantum Mechanics
4.1 The impact of Schrödinger’s and Dirac’s equations
4.2 Other approaches
4.3 Wave geometry
5 Born–Infeld Theory
6 Affine Geometry: Schrödinger as an Ardent Player
6.1 A unitary theory of physical fields
6.2 Semi-symmetric connection
7 Mixed Geometry: Einstein’s New Attempt
7.1 Formal and physical motivation
7.2 Einstein 1945
7.3 Einstein–Straus 1946 and the weak field equations
8 Schrödinger II: Arbitrary Affine Connection
8.1 Schrödinger’s debacle
8.2 Recovery
8.3 First exact solutions
9 Einstein II: From 1948 on
9.1 A period of undecidedness (1949/50)
9.2 Einstein 1950
9.3 Einstein 1953
9.4 Einstein 1954/55
9.5 Reactions to Einstein–Kaufman
9.6 More exact solutions
9.7 Interpretative problems
9.8 The role of additional symmetries
10 Einstein–Schrödinger Theory in Paris
10.1 Marie-Antoinette Tonnelat and Einstein’s Unified Field Theory
10.2 Tonnelat’s research on UFT in 1946 – 1952
10.3 Some further developments
10.4 Further work on unified field theory around M.-A. Tonnelat
10.5 Research by and around André Lichnerowicz
11 Higher-Dimensional Theories Generalizing Kaluza’s
11.1 5-dimensional theories: Jordan–Thiry theory
11.2 6- and 8-dimensional theories
12 Further Contributions from the United States
12.1 Eisenhart in Princeton
12.2 Hlavatý at Indiana University
12.3 Other contributions
13 Research in other English Speaking Countries
13.1 England and elsewhere
13.2 Australia
13.3 India
14 Additional Contributions from Japan
15 Research in Italy
15.1 Introduction
15.2 Approximative study of field equations
15.3 Equations of motion for point particles
16 The Move Away from Einstein–Schrödinger Theory and UFT
16.1 Theories of gravitation and electricity in Minkowski space
16.2 Linear theory and quantization
16.3 Linear theory and spin-1/2-particles
16.4 Quantization of Einstein–Schrödinger theory?
17 Alternative Geometries
17.1 Lyra geometry
17.2 Finsler geometry and unified field theory
18 Mutual Influence and Interaction of Research Groups
18.1 Sociology of science
18.2 After 1945: an international research effort
19 On the Conceptual and Methodic Structure of Unified Field Theory
19.1 General issues
19.2 Observations on psychological and philosophical positions
20 Concluding Comment

List of Biographies

Richard L. Arnowitt (1928 –) stayed at the Institute for Advanced Study in Princeton 1954 – 1956. Later Professor at Northeastern University in Boston and at Texas A&M University in College Station, Texas. There, “Distinguished Professor Emeritus” (2007). He co-developed the ADM-formalism essential for recasting Einstein-gravity into the Hamiltonian formalism. His publications include as diverse topics as the many body theory of liquid Helium and supergravity grand unification.
Gaganbihari Bandyopadhyay (? – ?). Formerly at Government College, Darjeeling, assistant professor of mathematics, Indian Institute of Technology, Kharakpur, and then Professor at the University of Calcutta in the Department of Applied Mathematics. Now retired.
Valentine Bargmann (1908 – 1989) was born in Berlin and began his studies there. In 1933, he moved to Zurich and received his doctorate with G. Wentzel. After his emigration to the United States he became assistant of A. Einstein at the Institute for Advanced Study (PIAS) from 1937 to 1946. From 1946 on he joined the faculty of Princeton University as a mathematician until retirement. Among his interests were the representation theory of SL (2,R ) and the foundation and applications of Hilbert space representations by holomorphic functions (Bargmann spaces) [332].
This is Satyendra Nath Bose (1894 – 1974) of the Einstein–Bose statistics.
Hans A. Buchdahl (1919 – 2010), born in Mainz, Germany; sent to London in 1933 for higher education by his parents in view of the Nazi rule. After having obtained his degree at the London College of Science, in 1939, he was detained as a German National and deported to Australia in 1940. His abilities in mathematics were recognized soon and he became teaching assistant at the University of Tasmania in Hobart, part-time lecturer and research physicist. He received a doctorate there in 1948 and a DSc from Imperial College, London, in 1956. As a reader in Tasmania, he was called to become professor and head of the Department of Theoretical Physics at the Australian National University, in 1963 until retirement in 1984. His broad interests included geometrical optics, thermodynamics, theories of gravitation as well as tensor and spinor analysis. He wrote well received books in all of these fields.
Albert Crumeyrolle (1919 – 1992), after his work on unified field theory, gave important contributions to spinor structures and Clifford algebras. He was Professor at the University Paul Sabatier in Toulouse.
Bruno Finzi (1899 – 1974). Graduation in 1919/20 in mathematics and industrial engineering at the University of Pavia. 1922 assistant of the mathematical physicist Umberto Cisotti at the Polytechnical Institute of Milano (Technical University). Professor of rational mechanics at the University of Milano in 1931 and later director of the mathematical Institute of the Politechnico. Contributions to classical fluid dynamics and aeronautics as well as to space-time-geometry. Established a sizeable school of reserchers in UFT.
Henry Thomas Flint (1890 – 1971) obtained a MSc from the University of Birmingham. After the first world war, he gained his DSc from the University of London while being a lecturer in physics at King’s College London. Flint was appointed Professor of Physics at Bedford University of London in 1944 and stayed thereuntil 1956.
Pierre-V. Grosjean (1912 – 2007), a Belgian mathematician, lived an uncommon life. After twenty years in the Congo as statistician for a mining business, meteorologist, and professor at a university there, he wrote his dissertation in Liège and then subsequently became a lecturer at the universities of Tunis, Caen and Rabat. He was elected full professor at the University of Mons, Belgium in 1968 where he stayed until retirement. He was also a writer with, among others, a book about his time in the Congo and three detective novels. He fought for the recognition of the Armenian genocide in Turkey after World War I.
Roland Guy(1919 – 2006). A Swiss mathematical physicist who had written a doctoral thesis in Paris and later taught at the University of Montreal. His specialty besides differential geometry was the field of integral equations.
Václav Hlavatý (1894 – 1969), mathematician, born in Czechoslovakia. PhD Charles University, Prague, 1922; post doctoral studies at universities in Holland, Rome, Paris and Oxford; professor of mathematics at Charles University, 1930 – 1948; visiting professor at Princeton University at the invitation of Albert Einstein, 1937 – 1938; a member of the Czech Socialist Party, entered politics in 1946; member of the Czech parliament in 1947; refused to sign Communist loyalty oath and left Czechoslovakia in 1948; taught one semester at the Sorbonne, 1948. In the fall of 1948 he accepted a professorship of mathematics at Indiana University. External Link
Pascual Jordan (1902 – 1980) was the only pioneer of quantum (matrix-) mechanics and quantum field theory who was not awarded a Nobel Prize unlike M. Born, W. Heisenberg and P. A. M. Dirac. After having been an assistant of R. Courant and M. Born in Göttingen and lecturer in Hamburg, in 1929 he became professor in Rostock; in 1944 he succeeded M. v. Laue at the (now Humboldt) University of Berlin. Due to his intellectual support of the Nazi-movement, after the second world war he had to wait until 1953 before again becoming full professor at the university of Hamburg. Apart from theoretical physics, Jordan also contributed to mathematics (Jordan algebras) and, less successfully, to biology and geology.
Bruria Kaufman(-Harris) (1918 – 2010) received an MA from Hebrew University (Jerusalem) in 1938 and a PhD from Columbia University, New York in 1948. During the late 1940s she collaborated with Lars Onsager, and then from 1950 until the mid 1950s with Albert Einstein. Her own interests were, e.g., the application of spinor analysis to physical problems, and special functions seen from the angle of Lie algebra. Her 2nd marriage, in 1996, with Nobel prize winner W. Lamb ended in divorce.
Behram Kursunŏglu (1922 – 2003) graduated from the University of Edinburgh and received his doctoral degree in physics at the University of Cambridge. During the period of 1956 – 1958, he served as the dean of the Faculty of Nuclear Sciences and Technology at Middle East Technical University, Ankara. He held several teaching positions in the United States and, since 1958, a professorship at the University of Miami. In 1965, he was one of the co-founders of the Center for Theoretical Studies of the University of Miami, of which he became the first director.
André Lichnerowicz (1915 – 1998). He received his doctorate with Georges Darmois on general relativity in 1939. First maître de conférences at the University of Strasbourg (transfered to Clermont-Ferrand during the German occupation), then in Paris; since 1949 professor at the faculty of science of the university of Paris. From 1952 until retirement in 1986 he held a chair for mathematical physics at the Collège de France in Paris. Member of the French Academy of Sciences since 1963. 1966 – 1973 president of Ministerial Commission on the Teaching of Mathematics.
J. McConnel (1915 – 1999), since 1968 senior professor at DIAS, 1969 to 1972 Director of the School of Theoretical Physics there.
Ratan Shanker Mishra (1918 – ?). Professor and Head of the Department of Mathematics at Gorakhpur and Allahabad from 1958 – 1963, and from 1963 – 1968. Head of the Department of Mathematics and Statistics at Banaras Hindu University in Varanasi since 1968. He has been a visiting professor in many countries, and worked and published with V. Hlavatý at Indiana University. His interests are well characterized by the title of his book Structures in a Differentiable Manifold (1978).
John Moffat (1932 –) He obtained his PhD with Fred Hoyle and Abdus Salam. He has been a physics professor at the University of Toronto and also an adjunct Professor in physics at the University of Waterloo. He is a resident affiliate member of the Perimeter Institute for Theoretical Physics, Waterloo, Canada. His interests are alternative theories of gravitation, cosmology and (non-local) quantum field theory.
Achilles Papapetrou (1907 – 1997) born in Northern Greece, had studied engineering in Athens. He received his PhD in theoretical physics 1935 at Technische Hochschule Stuttgart, Germany, under the supervision of Peter Paul Ewald. In 1946 – 1948 he became research fellow with Schrödinger at the Institute for Advanced Study in Dublin, later in Manchester (1948 – 1952) with P. M. S. Blackett; then professor at the Academy of Sciences, Berlin (1952 – 1961), and at the Institut Henri Poincaré, Paris 1960 – 1977.
Maria Pastori (1895 – 1975). After teaching at elementary school, she entered Scuola normale superiore di Pisa and graduated as number one. She continued teaching in middle school and in 1929 became regular assistant in mathematics at the University of Milano. With the exception of years at the University of Messina from 1934 to 1939, she spent her whole carrier at the university of Milano. Her contributions were mostly in tensor analysis and differential geometry but she also was interested in quantum mechanics and thermodynamics.
Julius Podolanski (1905 – 1955), born in Poland grew up in Germany (in what now is Thuringia) to where his parents had moved. He received his PhD at the university of Jena. After having been assistant there and then with W. Heisenberg in Leipzig, although a German citizen, due to his being of Jewish descent he could no longer work at a German university after 1933. Jobless at first, he then could join the publisher Akademische Verlagsgesellschaft, Leipzig and, when proofreading H. Kramers’ article on Grundlagen der Quantenmechanik, he discovered errors and suggested improvements. Thus he got into contact with the impressed author. In 1937 he wrote letters to M. Born, H. Kramers and E. Schrödinger and presented them a manuscript on a new theory aimed at “replacing Dirac’s theory of the electron.” It unfortunately yielded two further particles, one spinless, the other uncharged with spin 1/2. Kramers managed to get him a position as assistant at the University of Leiden. After hiding in Utrecht during the later years of the war, he afterwards obtained a position in Utrecht with L. Rosenfeld, and since 1948 joined him again in Manchester [517].
Erwin Rudolf Josef Alexander Schrödinger (1887 – 1961), Austrian theoretical physicist. He was the creator of quantum wave mechanics with his famous “Schrödinger equation” suggested in 1926. Nobel prize in 1933. Professor at the Universities of Stuttgart, Breslau, Zürich, Berlin, Graz, and Wien. Professor at and director of the Dublin School of Theoretical Physics between 1940 and 1956.
Dennis William S. Sciama (1926 – 1999) was a British physicist who had earned his PhD in 1953 at Cambridge University with Paul Dirac. He taught at Cornell, King’s College London, Harvard and the University of Texas at Austin, but mostly at Cambridge (1950s and 1960s) and the University of Oxford (1970s and early 1980s). In 1983, he became professor of Astrophysics at the International School of Advanced Studies (SISSA) in Trieste.
Hsin P. Soh (Shu Xingbei) (1905 – 1983), after an education at Chinese Universities, continued his physics and mathematics studies at the University of California in San Francisco, at Cambridge University (with Eddington), and then at the Massachusetts Institute of Technology (with D. J. Struik). He received the chair position in the Department of Mathematics of Jinan University (Shanghai) and became professor at Zhejiang University (Hangzhou). His most famous student is the Nobel Prize winner Tsung-Dao Lee. Soh was purged heavily as anti-revolutionary in 1958 and rehabilitated fully only in 1979.
Ernst Gabor Straus (1922 – 1983) had to leave his birthplace Munich in 1933 with his family. He obtained his doctorate in mathematics at Columbia University in New York (1948) with Albert Einstein as his second adviser. He became an assistant of Einstein at the Institute for Advanced Study from 1950 – 1953. He spent his later academic career at the University of California, Los Angeles.
Yves (René) Thiry (1915-); studied physics in Strasbourg with A. Lichnerowicz, and since the early 1960s became professor for physics at the astrophysical institute of the University of Paris, then professor for celestial mechanics at the University Paris VI, and corresponding member of the Academy.
Marie-Antoinette Tonnelat, née Baudot (1912 – 1980) first studied philosophy and then joined the group of theoretical physics around L. de Broglie at the Institut Henri Poincaré, in 1925. She wrote her PhD thesis with him on the “Theory of the photon in a Riemannian space” in 1939. The “second part” of the thesis was done under the supervision of Jean Perrin on “Artificial Radioactivity”. It seems that she received her degree only in 1941. Since 1956 she became Professeur à la Faculté des Sciences of the University of Paris (Sorbonne); in this faculty she thus joined her teacher L. de Broglie. Mme. Tonnelat held a diploma in the history of science and, since 1949 regularly taught courses in this field as well. She also created an interdisciplinary seminar on the History of Sciences. Among her publications in this field, a book on the history of the relativity principle is to be noted [645*]. In 1945 she received the prize “Pierson Perrin” and in 1970 the prize “Henri Poincaré” of the Academy of Sciences in Paris [418, 92*]. Tonnelat also published a volume of novellas.
Hans-Jürgen Treder (1928 – 2006) was a theoretical physicist with an interest in general relativity, cosmology and astrophysics. He headed the Central Institute for Astrophysics of the German Academy of Sciences and became director of its Cosmic Physics department.
Paolo Udeschini (1913 – 2006) Professor first at the University of Pavia (1950 – 1961); then professor for Rational Mechanics at the University of Milano.
Judith Winogradzki née Winterberg (1916 – 2006). She eventually became Professor of Theoretical Physics at the University of Rouen.
Robert C. Wrede (1926 – 2011) received his PhD in 1956 with Hlavatý. He became professor at San José State University, California, 1955 – 1994. Here, he concentrated on teaching and writing introductory mathematical textbooks. He was also active in university politics.
Max Wyman (1916 – 1991) PhD at the California Institute of Technology. Since 1941 lecturer in mathematics and since 1956 full professor at the University of Alberta, Edmonton. President of this university 1969 – 1974.
Hans Julius Zassenhaus (1912 – 1991) PhD 1934 University of Hamburg with Hecke and Artin. Refused professorship at the University of Bonn in 1941. 1949 – 1959 professor at McGill University, Montreal, then at the University of Notre Dame, Indiana, and since 1964 at Ohio State University.