Robert Hermann
Robert C. Hermann (April 28, 1931 â February 10, 2020) was an American mathematical physicist.
Books & Papers[edit]
Interdisciplinary Mathematics Series[edit]
Published by Math Sci Press, Brookline, Massachusetts
- General Algebraic Ideas (1973)
- Linear and Tensor Algebra (1973)
- Algebraic Topics in Systems Theory (1973)
- Energy-Momentum Tensors (1973)
- Topics in General Relativity (1973)
- Topics in the Mathematics of Quantum Mechanics (1973)
- Spinors, Clifford and Cayley Algebras (1974)
- Linear Systems and Introductory Algebraic Geometry (1974)
- Geometric Structure Theory of Systems-Control Theory and Physics, Part A (1974)
- Gauge Fields and CartanâEhresmann Connections (1975)
- Geometric Structure of Systems-Control Theory and Physics, Part B (1976)
- Geometric Theory of Non-Linear Differential Equations, Bäcklund Transformations, and Solitons, Part A (1976)
- Algebro-Geometric and Lie Theoretic Techniques in Systems Theory (with Clyde Martin) (1977)
- Geometric Theory of Non-Linear Differential Equations, Bäcklund Transformations, and Solitons, Part B (1976)
- Toda Lattices, Cosymplectic Manifolds, Bäcklund Transformations, and Kinks, Part A (1977)
- Quantum and Fermion Differential Geometry (1977)
- Differential Geometry and the Calculus of Variations, 2nd Edition (1977)
- Toda Lattices, Cosymplectic Manifolds, Bäcklund Transformations, and Kinks, Part B (1977)
- YangâMills, KaluzaâKlein, and the Einstein Program (with contributions by Frank Estabrook, Hugo Wahlquist) (1978)
- Cartanian Geometry, Nonlinear Waves, and Control Theory, Part A (1979)
- Cartanian Geometry, Nonlinear Waves, and Control Theory, Part B (1980)
- Topics in the Geometric Theory of Linear Systems (1984)
- Topics in the Geometric Theory of Integrable Dynamical Systems (1984)
- Topics in Physical Geometry (1988)
- Geometric Computing Science â First Steps (1991)
- Geometric Structures in Nonlinear Physics (1991)
- Constrained Mechanics and Lie theory (1992)
- LieâCartanâEhresmann Theory (1993)
- Lie-theoretic Ordinary Differential Equations, Numerical Analysis, Mechanics, and Differential Systems (1994)
- CâOâR Generalized Functions, Current Algebras and Control (1994)
Lie Groups Series: History, Frontiers and Applications[edit]
- Sophus Lie's 1880 Transformation Group Paper. Translation by M. Ackerman. Appendices by R. Hermann
- Ricci and Levi-Civita's Tensor Analysis Paper. Translation and comments by R. Hermann
- Sophus Lie's 1884 Differential Invariants Paper. Translation by M. Ackerman. Appendices by R. Hermann
- Smooth Compactification of Locally Symmetric Varieties. By A. Ash, D. Mumford, M. Rapoport and Y. Tal
- Simplectic Geometry and Fourier Analysis. By N. Wallach. Appendix on Quantum Mechanic by R. Hermann
- The 1976 AMES Research Center (NASA) Conference on Geometric Nonlinear Wave Theory. Edited by R. Hermann
- The 1976 AMES Research Center (NASA) Conference on Geometric Control Theory. Edited by R. Hermann and Clyde Martin
- Hilbert's Papers on Invariant Theory. Translated by M. Ackerman, comments by R. Hermann
- Development of Mathematics in the 19th Century. By Felix Klein. Translated by M. Ackerman. Appendix: "Kleinian Mathematics from an Advanced Standpoint" by R. Hermann
- Quantum Statistical Mechanics and Lie Group Harmonic Analysis. By Norman Hurt and Robert Hermann (1980)
- First Workshop on Grand Unification. Editors: P. Frampton, S. Glashow and A. Yildiz
- Inverse Scattering Papers: 1955-1963. By Irvin Kay and Harry E. Moses
- Geometry of Riemannian Spaces. By Elie Cartan. Translation by James Glazebrook, Appendices by Robert Hermann
- The Geometric Theory of Ordinary Differential Equations. By Georges Valiron. Translation by James Glazebrook
- The Classical Differential Geometry of Curves and Surfaces. By Georges Valiron. Translation by James Glazebrook
Systems Information and Control[edit]
- Geometry and Identification: Proceedings of APSM Workshop on System Geometry, System Identification, and Parameter Identification. Editors: Peter Canes and Robert Hermann
- Berkeley-Ames Workshop on Nonlinear Problems in Control and Fluid Mechanics. Editors: L. R. Hunt and C. F. Martin
Other Works[edit]
- Lie algebras and quantum mechanics, Benjamin, Inc (1970)
- Geometry, Physics and Systems, Dekker (1973)
- Differential geometric methods and ideas in physics and engineering, Rutgers University Press, (1973)
- Compactifications of Homogeneous Spaces and Contractions of Lie Groups, PNAS, (1964)
- Lie Groups for Physicists, Addison-Wesley Publication Co (1966)
- Fourier Analysis on Groups and Partial Wave Analysis, Benjamin, Inc (1969)
- Lectures in Mathematical Physics, Benjamin, Inc (1970)
- Vector Bundles in Mathematical Physics, Vol. 1, Benjamin, Inc (1970)
- Vector Bundles in Mathematical Physics, Vol. 2, Benjamin, Inc (1970)
- Physical Aspects of Lie Group Theory, Les Presses de l'university de Montreal (1974)
- Ames Research Center Publications, (1977)
- Nonlinear Controllability and Observability, IEEE Transactions on Automatic Control (1977)
Eric on Hermann[edit]
The first talk I ever gave revealing the Physics I was actually working on @ Harvard/MIT was at MIT at the insistence of the great Isadore Singer. The one man who *fully* understood what I said came to me afterwards & insisted we speak. He seemed half mad: https://www.math.columbia.edu/~woit/wordpress/?p=11608
His name was Robert Hermann. I couldn't tell what was going on. He was very excited & wanted to be of any help possible. It was almost terrifying as I was not eager to discuss the work. When I told Singer about it, Singer said "That's a high compliment. Do you know who that is?"
I told Is "I know him from an enormous number of self-published books only" Then the great MIT Professor said: "Eric, that is the first man to figure out that quantum field theory is based on the geometry of Fiber Bundles before Simons, Wu, Yang & I did our work."
I was floored.
This odd man, working outside the University system, outside Peer Review, and outside normal publishing was held in awe by the TOP Mathematician at MIT. The system knew who it had lost and revered him as a serious mind; a man with a viable claim to an earth shattering discovery.
It simultaneously filled me with fear & hope. This odd man was not a nut or lunatic. I had spoken to a true maverick & he had seen me like no one else...even beyond my good friend Is Singer. Years later I tried to contact him but he was in an old age home with dementia. All lost.
A missed moment. I was too scared to leave the damned university system behind me with all of its rules and enforced rituals. I knew what he represented: freedom, genius and irrelevancy except for the tiny number of people at the absolute top of the field.
I was too cowardly.
Robert: I never got the chance to "Thank You" for believing in me and your offer of help. My bad. So thank you.
RIP: Robert C. Hermann (April 28, 1931 â February 10, 2020) Maverick and Likely discoverer of the Geometric Basis of the Quantum Field Theory of the Standard Model.
