Background
Carroll, Robert Wayne was born on May 10, 1930 in Chicago, Illinois, United States. Son of Walter Scott and Dorothy (Le Monnier) Carroll.
(About four years ago a prominent string theorist was quot...)
About four years ago a prominent string theorist was quoted as saying that it might be possible to understand quantum mechanics by the year 2000. Sometimes new mathematical developments make such understanding appear possible and even close, but on the other hand, increasing lack of experimental verification make it seem to be further distant. In any event one seems to arrive at new revolutions in physics and mathematics every year. This book hopes to convey some of the excitment of this period, but will adopt a relatively pedestrian approach designed to illuminate the relations between quantum and classical. There will be some discussion of philosophical matters such as measurement, uncertainty, decoherence, etc. but philosophy will not be emphasized; generally we want to enjoy the fruits of computation based on the operator formulation of QM and quantum field theory. In Chapter 1 connections of QM to deterministic behavior are exhibited in the trajectory representations of Faraggi-Matone. Chapter 1 also includes a review of KP theory and some preliminary remarks on coherent states, density matrices, etc. and more on deterministic theory. We develop in Chapter 4 relations between quantization and integrability based on Moyal brackets, discretizations, KP, strings and Hirota formulas, and in Chapter 2 we study the QM of embedded curves and surfaces illustrating some QM effects of geometry. Chapter 3 is on quantum integrable systems, quantum groups, and modern deformation quantization. Chapter 5 involves the Whitham equations in various roles mediating between QM and classical behavior. In particular, connections to Seiberg-Witten theory (arising in N = 2 supersymmetric (susy) Yang-Mills (YM) theory) are discussed and we would still like to understand more deeply what is going on.
http://www.amazon.com/gp/product/0444541985/?tag=2022091-20
(When soliton theory, based on water waves, plasmas, fiber...)
When soliton theory, based on water waves, plasmas, fiber optics etc, was developing in the 1960-1970 era it seemed that perhaps KdV (and a few other equations) were really rather special in the set of all interesting partial differential equations. As it turns out, although integrable systems are still special, the mathematical interaction of integrable systems theory with virtually all branches of mathematics (and with many currently developing areas of theoretical physics) illustrates the importance of this area. This book concentrates on developing the theme of the tau function. KdV and KP equations are treated extensively, with material on NLS and AKNS systems, and in following the tau function theme one is led to conformal field theory, strings, and other topics in physics. The extensive list of references contains about 1000 entries.
http://www.amazon.com/gp/product/0444548777/?tag=2022091-20
( This self-contained text is directed to graduate studen...)
This self-contained text is directed to graduate students with some previous exposure to classical partial differential equations. Readers can attain a quick familiarity with various abstract points of view in partial differential equations, allowing them to read the literature and begin thesis work. The author's detailed presentation requires no prior knowledge of many mathematical subjects and illustrates the methods' applicability to the solution of interesting differential problems. The treatment emphasizes existence-uniqueness theory as a topic in functional analysis and examines abstract evolution equations and ordinary differential equations with operator coefficients. A concluding chapter on global analysis develops some basic geometrical ideas essential to index theory, overdetermined systems, and related areas. In addition to exercises for self-study, the text features a thorough bibliography. Appendixes cover topology and fixed-point theory in addition to Banach algebras, analytic functional calculus, fractional powers of operators, and interpolation theory.
http://www.amazon.com/gp/product/0486488357/?tag=2022091-20
(About four years ago a prominent string theorist was quot...)
About four years ago a prominent string theorist was quoted as saying that it might be possible to understand quantum mechanics by the year 2000. Sometimes new mathematical developments make such understanding appear possible and even close, but on the other hand, increasing lack of experimental verification make it seem to be further distant. In any event one seems to arrive at new revolutions in physics and mathematics every year. This book hopes to convey some of the excitment of this period, but will adopt a relatively pedestrian approach designed to illuminate the relations between quantum and classical. There will be some discussion of philosophical matters such as measurement, uncertainty, decoherence, etc. but philosophy will not be emphasized; generally we want to enjoy the fruits of computation based on the operator formulation of QM and quantum field theory. In Chapter 1 connections of QM to deterministic behavior are exhibited in the trajectory representations of Faraggi-Matone. Chapter 1 also includes a review of KP theory and some preliminary remarks on coherent states, density matrices, etc. and more on deterministic theory. We develop in Chapter 4 relations between quantization and integrability based on Moyal brackets, discretizations, KP, strings and Hirota formulas, and in Chapter 2 we study the QM of embedded curves and surfaces illustrating some QM effects of geometry. Chapter 3 is on quantum integrable systems, quantum groups, and modern deformation quantization. Chapter 5 involves the Whitham equations in various roles mediating between QM and classical behavior. In particular, connections to Seiberg-Witten theory (arising in N = 2 supersymmetric (susy) Yang-Mills (YM) theory) are discussed and we would still like to understand more deeply what is going on. Thus in Chapter 5 we will try to give some conceptual background for susy, gauge theories, renormalization, etc. from both a physical and mathematical point of view. In Chapter 6 we continue the deformation quantization then by exhibiting material based on and related to noncommutative geometry and gauge theory.
http://www.amazon.com/gp/product/0444506217/?tag=2022091-20
Carroll, Robert Wayne was born on May 10, 1930 in Chicago, Illinois, United States. Son of Walter Scott and Dorothy (Le Monnier) Carroll.
Bachelor of Science, University Wisconsin, 1952; Doctor of Philosophy, University Maryland., 1959.
Aero. research scientist, National Aeronautics and Space Administration, Cleveland, 1952-1954; National Science Foundation postdoctoral fellow, 1959-1960; assistant professor, Rutgers University, 1960-1963; associate professor, Rutgers University, 1963-1964; associate professor mathematics, University of Illinois, Urbana, 1964-1967; professor, University of Illinois, Urbana, 1967-1997; professor emeritus, University of Illinois, Urbana, since 1997.
(When soliton theory, based on water waves, plasmas, fiber...)
(About four years ago a prominent string theorist was quot...)
(About four years ago a prominent string theorist was quot...)
( This self-contained text is directed to graduate studen...)
Served with United States Army, 1954-1957. Member American Mathematics Society, American Physical Society.
Married Berenice Jacobs, September 7, 1957 (divorced June 1974). Children: David Leon, Malcolm Scott. Married Alice von Neumann, September 1974 (divorced March 1977).
Married Joan Miller, January 1979 (deceased April 2001), Married Denise Bredt, May 2003.