The field tensor was introduced by a mathematician and professor who had taught at which three universities?
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Electromagnetic tensor In electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in spacetime. The field tensor was first used after the four-dimensional tensor formulation of special relativity was introduced by Hermann Minkowski. The tensor allows related physical laws to be written very concisely.
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Hermann Minkowski Hermann Minkowski ( ; ] ; 22 June 1864 – 12 January 1909) was a mathematician and professor at Königsberg, Zürich and Göttingen. He created and developed the geometry of numbers and used geometrical methods to solve problems in number theory, mathematical physics, and the theory of relativity.
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Spinor In geometry and physics, spinors are elements of a (complex) vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a slight (infinitesimal) rotation. When a sequence of such small rotations is composed (integrated) to form an overall final rotation, however, the resulting spinor transformation depends on which sequence of small rotations was used: "unlike" vectors and tensors, a spinor transforms to its negative when the space is rotated through a complete turn from 0° to 360° (see picture). This property characterizes spinors. It is also possible to associate a substantially similar notion of spinor to Minkowski space in which case the Lorentz transformations of special relativity play the role of rotations. Spinors were introduced in geometry by Élie Cartan in 1913. In the 1920s physicists discovered that spinors are essential to describe the intrinsic angular momentum, or "spin", of the electron and other subatomic particles.
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H. Dieter Zeh Heinz-Dieter Zeh (] ; born 8 May 1932 in Braunschweig, Germany), usually referred to as H. Dieter Zeh, is a professor emeritus of the University of Heidelberg and theoretical physicist.
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Werner Döring Werner Döring (2 September 1911, Berlin – 6 June 2006, Malente) was a German theoretical physicist. From 1963 until his retirement in 1977, he was ordinary professor at the University of Hamburg. His main interest was the theory of magnetism. His textbooks on theoretical physics have influenced several generations of students.
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Stephanie B. Alexander Stephanie Brewster Brewer Taylor Alexander is an American mathematician, a professor emerita of mathematics at the University of Illinois at Urbana–Champaign. Her research concerns differential geometry and metric spaces.
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Domina Eberle Spencer Domina Eberle Spencer (born September 26, 1920) is a mathematician at the University of Connecticut who works on electrodynamics and field theory. She earned her Ph.D. in 1942 from the Massachusetts Institute of Technology under the supervision of Dirk Jan Struik.
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David Hilbert David Hilbert (] ; 23 January 1862 – 14 February 1943) was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.
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Paul Funk Paul Georg Funk (14 April 1886, Vienna – 3 June 1969, Vienna) was an Austrian mathematician who introduced the Funk transform and who worked on the calculus of variations. He was one of David Hilbert's students.
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Maxwell stress tensor The Maxwell stress tensor (named after James Clerk Maxwell) is a second-order tensor used in classical electromagnetism to represent the interaction between electromagnetic forces and mechanical momentum. In simple situations, such as a point charge moving freely in a homogeneous magnetic field, it is easy to calculate the forces on the charge from the Lorentz force law. When the situation becomes more complicated, this ordinary procedure can become impossibly difficult, with equations spanning multiple lines. It is therefore convenient to collect many of these terms in the Maxwell stress tensor, and to use tensor arithmetic to find the answer to the problem at hand.
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Carl Friedrich Gauss Johann Carl Friedrich Gauss ( ; German: "Gauß" , ] ; Latin: "Carolus Fridericus Gauss" ) (30 April 177723 February 1855) was a German mathematician who contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, mechanics, electrostatics, magnetic fields, astronomy, matrix theory, and optics.
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Ray Streater Raymond Frederick "Ray" Streater (born 1936) is a British physicist, and professor emeritus of Applied Mathematics at King's College London. He is best known for co-authoring a text on quantum field theory, the 1964 ""PCT, Spin and Statistics and All That.""
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Vasily Vladimirov Vasilii Sergeevich Vladimirov (Russian: Васи́лий Серге́евич Влади́миров ) (9 January 1923 – 3 November 2012) was a Soviet mathematician and mathematical physicist working in the fields of number theory, mathematical physics, quantum field theory, numerical analysis, generalized functions, several complex variables, p-adic analysis, multidimensional tauberian theorems.
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Robert Bartnik Robert Bartnik is an Australian mathematician based at Monash University, where he holds the position of Professor of Pure Mathematics. He is known for his contribution to general relativity, particularly for demonstrating that the ADM mass of an asymptotically flat spacetime is a well-defined quantity. He gained his bachelor's and master's degrees from Melbourne University and his PhD from Princeton University in 1983. His dissertation subject was "Existence of Maximal Hypersurfaces". In 2004 he was elected as a fellow of the Australian Academy of Science at which time it was noted He is perhaps best known for his work with John McKinnon on particle-like solutions of the Einstein Yang–Mills equation, but he has worked widely on applications of geometry and analysis to the study of spacetime structure.
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Michael Artin Michael Artin (] ; born 28 June 1934) is an American mathematician and a professor emeritus in the Massachusetts Institute of Technology mathematics department, known for his contributions to algebraic geometry.
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Wolfhart Zimmermann Zimmermann was born in Freiburg im Breisgau. In the 1950s he was at Göttingen one of the pioneers of the mathematical quantum field theory; along with Kurt Symanzik and Harry Lehmann he developed the LSZ theory. From 1962 to 1974 he was a professor at the New York University. From 1974 to 1996 he was a director at the Max Planck Institute for physics in Munich, where he was later "Director Emeritus".
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Svetozar Kurepa Svetozar Kurepa (May 25, 1929 – February 2, 2010) was a mathematician whose main contributions were in the areas of functional analysis and operator theory. Kurepa published over 70 articles, 16 books, and numerous scientific reviews. He taught at the University of Zagreb, where he also served as the Dean of the College of Sciences. He taught in North America at the University of Maryland, at Georgetown University, and at the University of Waterloo. In Europe he worked at the Niels Bohr Institute in Denmark and the University of Milan.
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Field theory (psychology) Field theory is a psychological theory (more precisely: Topological and vector psychology) which examines patterns of interaction between the individual and the total field, or environment. The concept first made its appearance in psychology with roots to the holistic perspective of Gestalt theories. It was developed by Kurt Lewin, a Gestalt psychologist, in the 1940s.
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Nicolae Popescu Nicolae Popescu, Ph.D., D.Phil. (] ; 22 September 1937 – 29 July 2010) was a Romanian mathematician and Emeritus Professor. Popescu was elected a Member of the Romanian Academy in 1992. He is best known for his contributions to Algebra and the theory of Abelian categories. Since 1964 and until 2007 he collaborated on the characterization of abelian categories with the well-known French mathematician Pierre Gabriel. His areas of expertise were: Category theory, Abelian categories with Applications to Rings and Modules, adjoint functors, limits/colimits, Theory of Sheaves, Theory of Rings, Fields and Polynomials, and Valuation Theory; he also had interests and published in the following areas: Algebraic Topology, Algebraic Geometry, Commutative Algebra, K-Theory, Class-Field theory, and Algebraic Function Theory. He published between 1962 and 2008 more than 102 papers in peer-reviewed, mathematics journals, several monographs on the theory of sheaves, and also six books on abelian category theory and abstract algebra. In a Grothendieck-like, energetic style, he initiated and provided scientific leadership to several seminars on category theory, sheaves and abstract algebra which resulted in a continuous stream of high-quality mathematical publications in international, peer-reviewed mathematics journals by several members participating in his Seminar series. His book "Abelian Categories with Applications to Rings and Modules" continues to provide valuable information to mathematicians around the world. His latest contributions have also branched into valuation and number theory. He has published over 110 original, peer-reviewed articles in mathematics, mostly in category theory, algebraic geometry, and Galois and number theory.
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John D. Barrow John David Barrow FRS (born 29 November 1952) is an English cosmologist, theoretical physicist, and mathematician. He is currently Research Professor of Mathematical Sciences at the University of Cambridge. Barrow is also a writer of popular science and an amateur playwright.
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Ruth Gregory Ruth Ann Watson Gregory is a British mathematician and physicist, currently Professor of Mathematics and Physics at the University of Durham. Her fields of specialisation are general relativity and cosmology.
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John Clayton Taylor John Clayton Taylor {'1': ", '2': ", '3': ", '4': "} (born 4 August 1930) is a British mathematical physicist. He is an Emeritus Professor of Mathematical Physics at the Department of Applied Mathematics and Theoretical Physics of the University of Cambridge and an Emeritus Fellow of Robinson College.