Robert Hermann (mathematician)
Robert Hermann ( born April 28, 1931 in Brooklyn ) is an American mathematician and mathematical physicist.
Hermann studied in Paris and at Princeton University ( where he attended lectures, among others, by Charles Ehresmann ), where he received his doctorate in 1955 with Donald Spencer (The differential geometry of homogeneous spaces ). He taught at Rutgers University, left this in 1975 and did research afterwards especially with financial means of the Ames Research Center of NASA. 1969/70 he was at the Institute for Advanced Study.
Hermann has published numerous books on differential geometry (especially after the French school of Elie Cartan ) and Lie groups theory and their applications to differential equations, integrable systems, control theory and physics, usually when he founded Mathematical Science Press in Brookline, Massachusetts, came out. He also stressed the historical component and were also works of Sophus Lie, Gregorio Ricci and Tullio Levi -Civita Curbastro, Felix Klein's lectures on the history of mathematics, Elie Cartan, Georges Valiron and invariantentheoretische work of David Hilbert with comment out again.
In the 1960s he focused on elementary particle physics and quantum field theory. Already in the 1960s he published books in which he exposed the context of the theory of fiber bundles on Riemannian manifolds with physics ( gauge theories ), which only later in the 1970s " common property " was in the physical sciences.
- Lie groups for physicists, Benjamin 1966
- Fourier analysis on groups and partial wave analysis, Benjamin 1969
- Lie algebras and quantum mechanics, Benjamin 1970
- Lectures in mathematical physics, Benjamin 1970
- Vector bundles in mathematical physics, Benjamin 1970
- Geometry, Physics and Systems, Dekker 1973
- Differential geometry and the calculus of variations, Academic Press 1968, 2nd edition 1977 Brookline
- Differential geometric methods and ideas in physics and engineering, Rutgers University Press, 1973
- Physical Aspects of Lie group theory, Montreal, press Universitaire de Montreal, 1974
In the Mathematical Science Press, Brookline, Massachusetts:
- Topics in the mathematics of quantum mechanics, Brookline, 1973, 1977
- With Clyde Martin: algebro - geometric and Lie theoretic techniques in control theory, Brookline 1977
- Algebraic topics in system theory, Brookline 1973
- General algebraic ideas, Brookline 1973
- Topics in General Relativity, Brookline 1973
- Energy - momentum tensor, Brookline 1973
- Cartanian geometry, nonlinear waves and control theory, Brookline, 2 parts 1980 ( Cartanian thinks in terms of Elie Cartan )
- Geometric structure theory of systems- control theory and physics, Brookline 1974
- Constrained mechanics and Lie theory, Brookline 1992
- Topics in the geometric theory of linear systems, Brookline 1984
- Yang - Mills, Kaluza-Klein and the Einstein program, Brookline 1978 (with contributions by Frank Estabrook, Hugo Wahlquist )
- Topics in the geometric theory of integrable dynamical systems, Brookline 1984
- Linear and tensor algebra, Brookline 1973
- Gauge fields and Cartan - Ehresmann Connections, Brookline 1975
- Topics in physical geometry, Brookline 1988
- With Norman Hurt: Quantum statistical mechanics and Lie group harmonic analysis, Brookline 1980
- Toda lattices, cosymplectic manifolds, Bäcklund transformations, and kinks, Brookline 1977
- The geometry of non- linear differential equations, Bäcklund transformations, and solitons, Brookline 1977
- Geometric structures in nonlinear systems, Brookline 1991 (including hydrodynamics, deformation structures, with a list of publications by Hermann to 1991)
- Spinor, Clifford and Cayley Algebras, Brookline 1974
- Linear systems and introductory algebraic geometry, Brookline 1974
- Lie - Cartan - Ehresmann Theory, Brookline 1993
- Lie - theoretic ordinary differential equations, numerical analysis, mechanics, and differential systems, Brooklyn 1994
- COR generalized functions, current algebras and control, Brookline 1994
- Geometric computing science - first steps, Brookline 1991
- Quantum and fermion differential geometry, Brookline 1977