Robert C. Hermann (April 28, 1931 – February 10, 2020) was an American mathematician and mathematical physicist. In the 1960s Hermann worked on elementary particle physics and quantum field theory, and published books which revealed the interconnections between
vector bundles on
Riemannian manifold
In differential geometry, a Riemannian manifold or Riemannian space , so called after the German mathematician Bernhard Riemann, is a real manifold, real, smooth manifold ''M'' equipped with a positive-definite Inner product space, inner product ...
s and
gauge theory
In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie groups) ...
in physics, before these interconnections became "common knowledge" among physicists in the 1970s.
Biography
Born in
Brooklyn, Hermann studied in Paris and at
Princeton University, where he attended lectures by
Charles Ehresmann
Charles Ehresmann (19 April 1905 – 22 September 1979) was a German-born French mathematician who worked in differential topology and category theory.
He was an early member of the Bourbaki group, and is known for his work on the differential ...
and where in 1955 under
Donald Spencer he received his PhD with thesis ''The Differential geometry of homogeneous spaces''. He was a Benjamin Peirce Instructor at
Harvard University in 1957, and researcher at
MIT Lincoln Laboratory 1959 to 61 when he lectured at
University of California Berkeley. In 1962 he became an
associate professor
Associate professor is an academic title with two principal meanings: in the North American system and that of the ''Commonwealth system''.
Overview
In the ''North American system'', used in the United States and many other countries, it is a ...
at
Northwestern University and was raised to full professor. In 1967 he taught at
University of California Santa Cruz until moving to
Rutgers University (1970 to 75). Subsequently he did research primarily with financial support from the
Ames Research Center of
NASA. In the academic year 1969/1970 he was at the
Institute for Advanced Study.
Following the French school of
Élie Cartan, Hermann published numerous books on
differential geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...
and
Lie group
In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additio ...
theory and their applications to differential equations, integrable systems, control theory, and physics. Most of these books were published in Brookline, Massachusetts by Math Sci Press, which he founded. Two series were published: a green series "Interdisciplinary Mathematics" and a blue series "Lie Groups: History, Frontiers and Applications".
The blue series considered history of differential geometry and
Lie theory, and edited, with extensive new commentary, the work of
Sophus Lie,
Gregorio Ricci-Curbastro and
Tullio Levi-Civita,
Felix Klein's ''Vorlesungen über Mathematikgeschichte'', Élie Cartan,
Georges Valiron
Georges Jean Marie Valiron (7 September 1884 – 17 March 1955) was a French mathematician, notable for his contributions to analysis, in particular, the asymptotic behaviour of entire functions of finite order and Tauberian theorems.
Biography
...
and the contributions to invariant theory by
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...
.
Robert Hermann died on February 10, 2020.
Early works
* 1966
''Lie Groups for Physicists'' Benjamin
* 1968: ''Differential geometry and the calculus of variations'', Academic Press, second edition, Brookline 1977
* 1969: ''Fourier analysis on groups and partial wave analysis'', Benjamin
* 1970: ''Lie algebras and quantum mechanics'', Benjamin
* 1970: ''Lectures in mathematical physics'', Benjamin
* 1970: ''Vector Bundles in mathematical physics'', Benjamin 1970
* 1973: ''Geometry, Physics and Systems'', Dekker
* 1973: ''Differential geometric methods and ideas in physics and engineering'', Rutgers University Press
* 1974: ''Physical Aspects of Lie group theory'', Montreal, Presse Universitaire de Montreal
Published by Math Sci Press, Brookline, Massachusetts
* 1973, 1977: ''Topics in the mathematics of quantum mechanics''
* 1973: ''Algebraic topics in systems theory''
* 1973: ''General algebraic ideas''
* 1973: ''Topics in General Relativity''
* 1973: ''Energy-Momentum Tensors''
* 1973: ''Linear and tensor algebra''
* 1974: ''Spinors, Clifford and Cayley Algebras''
* 1974: ''Linear systems and introductory algebraic geometry''
* 1974: ''Geometric structure theory of systems-control theory and physics''
* 1975: ''Gauge fields and Cartan–Ehresmann Connections''
* 1977: ''The geometry of non-linear differential equations, Bäcklund transformations, and solitons''
* 1977: (with
Clyde Martin
Clyde E. Martin (January 2, 1918 – December 5, 2014) was an American sexologist. He was an assistant to Alfred Kinsey on the Kinsey Reports and served as a co-author on ''Sexual Behavior in the Human Male'' and ''Sexual Behavior in the Human F ...
): ''Algebro-geometric and Lie theoretic techniques in systems theory''
* 1977: ''Toda lattices, cosymplectic manifolds, Bäcklund transformations, and kinks''
* 1977: ''Quantum and fermion differential geometry''
* 1978: (with contributions by Frank Estabrook, Hugo Wahlquist) ''Yang–Mills, Kaluza–Klein, and the Einstein program''
* 1979: ''Cartanian geometry, nonlinear waves, and control theory'', Brookline, 2 parts: Part A, Part B 1980
(''Cartanian'' meant in the sense of Élie Cartan)
* 1980: (with Norman Hurt) ''Quantum statistical mechanics and Lie group harmonic analysis''
* 1984: ''Topics in the geometric theory of linear systems''
* 1984: ''Topics in the geometric theory of integrable dynamical systems''
* 1988: ''Topics in physical geometry''
* 1991: ''Geometric computing science – first steps''
* 1991: ''Geometric structures in nonlinear systems'', Brookline 1991 (including hydrodynamics, deformation structures, with list of publications by Hermann to 1991)
* 1992: ''Constrained mechanics and Lie theory''
* 1993: ''Lie–Cartan–Ehresmann Theory''
* 1994: ''Lie-theoretic ordinary differential equations, numerical analysis, mechanics, and differential systems''
* 1994: ''C–O–R generalized functions, current algebras and control''
References
External links
Books from Math-sci Press*
* Peter Cains & 7 others (2021
Memorial for Robert Hermann ''
Notices of the American Mathematical Society''
{{DEFAULTSORT:Hermann, Robert
20th-century American mathematicians
21st-century American mathematicians
20th-century American physicists
1931 births
2020 deaths
American textbook writers
American historians of mathematics