Meinhard E. MayerProfessor Emeritus, Physics & Astronomy 

Research Interests 
Mathematical Physics; Quantum Theory of Gauge Fields, Applications of Differential Geometry to Physics, Wavelet Transforms and Applications to Turbulence. Computational Physics: Symbolic and Numerical Computation in Scheme. Linux and applications.  
URLs  www.physics.uci.edu/faculty/mayer.html  
Online copy of "Structure and Interpretation of Classical Mechanics"  
Academic Distinctions  College de France Medal, 1985  
Appointments  Joint Institute for Nuclear Research, Dubna, USSR, 19571958  
Research Abstract 
Professor Mayer earned a MS in Electrical Engineering from the Polytechnic Institute Bucharest (1952), and a Ph.D. in Mathematical Physics (1957) from Parhon University, Bucharest (both in Romania). He was on the faculty of both these institutions. He held a postdoctoral position at the Joint Institute for Nuclear Research at Dubna, Russia, and was on the faculties of Brandeis University and Indiana University, before joining the UCI Physics and Mathematics Departments in 1966. He has held visiting positions at (among others) the University of Vienna (Austria), Imperial College (London), CERN, Geneva, College de France, Institute des Hautes Etudes Scientifiques, Ecole Normale Superieure (France) the Universities of Hamburg, Koln and Bonn (Germany), Hebrew University, Tel Aviv University, and the Weizmann Institute (Israel), University of Rome (Italy), and Harvard, MIT, Princeton University, Rutgers University, and NYU. During the last three decades, Professor Mayer's research interests have ranged from applications of differential geometry to gauge theories, to wavelet analysis of atmospheric turbulence, and symbolic computation applied to physics. Differential geometric methods are playing an everincreasing role in mathematical physics, and in particular in particle theory and relativity. Professor Mayer was one of the pioneers in the use of the fiberbundle description of gauge theories and has written one of the earliest texts on the subject. He has done research on the applications of groupoids in gauge theory. During the past few years, wavelet transform methods have become a very popular topic in applied mathematics and computation. A family of wavelets is generated from a "motherwavelet" by scaling and translation and serves to decompose functions which exhibit selfsimilarity and scaling properties into spectra which can reveal interesting information about regions where significant changes in the "signal" occur. Professor Mayer has recently supervised two Ph.D. students who have applied wavelet transform methods respectively to pattern recognition in the IrvineMichiganBrookhaven proton decay experiment (E. Lulofs), and a wavelet crossspectral analysis of turbulence (L. Hudgins). The latter method has been applied to an analysis of flows in the boundary layers between atmosphere and ocean and atmosphere and land, have revealed interesting largescale coherent structures which are being investigated in a collaboration with Dr. L. Hudgins and Prof. Carl Friehe (ME). In the area of computational physics, Professor Mayer is collaborating with two colleagues at MIT in developing a mathematical library implemented in the Scheme dialect of Lisp, which is useful in symbolic and numerical computations using differentialgeometric methods. In particular, they have published a book on how to do Lagrangian and Hamiltonian mechanics within this framework. Recent research interests are related to understanding the role of ghosts in "causal perturbation theory" and the relation of Loop Quantum Gravity to gauge theories. Professor Mayer has been teaching both undergraduate and graduate courses in Mathematical Physics, and has developed a computational physics course and lab, making use of the Scheme programming language. He has some expertise in Linux and Mac OS X system administration and software development. He has recently been teaching Freshman Seminars, mainly related to quantum and particle physics. Outside of physics Professor Mayer has devoted some time to Yiddish and German poets and writers from Bukovina (where he grew up), and has offered a course on this subject at the Academy of Lifelong Learning. 

Publications  Quantum Fields and Elementary Particles (in Romanian), Editura Tehnica, Bucharest, 1959  
Introduction to the FiberBundle Approach to Gauge Theories (138 pages) in Lecture notes in Physics, vol 67, Springer Verlag New York, 1977 

"Structure and Interpretation of Classical Mechanics" with Gerald J. Sussman and Jack Wisdom (MIT),534 pages. MIT Press,Cambridge, MA, 2001.  
"Lie Groupoids versus Principal Bundles in Gauge Theories," in Proceedings of the International Conference on DifferentialGeometric Methods in Physics, L.L. Chau and W. Nahm, Eds., Plenum Press, 1990. 

"From Poisson Groupoids to Quantum Groupoids, and Back," in Proceedings of the XIX International Conference on DifferentialGeometric Methods in Physics, R. Cianci and U. Bruzzo, Eds. Rapallo, 1990; 12 pages, Springer Verlag, Heidelberg, 1991. 

"Wavelet and Fourier Analysis of Atmospheric Turbulence", with L. Hudgins, C. Friehe, in Proc. Intern. Conf. on Wavelets, Toulouse, 1992, pp. 491498; Y. Meyer and S. Roques, Eds., Frontieres, Gif, 1993. 

The MIT Scheme Math Library "nscmutils" Reference Manual with Gerald J. Sussman, 1999  
Professional Societies 
Fellow, American Physical Society, since 1967 Lifetime Member, American Mathematical Society, International Association of Mathematical Physics 

Other Experience 
Visiting Professor College de France 1985—1985 

Visiting Professor Institut des Hautes Etudes Scientifiques 1969—1970 

Visiting Professor University of Hamburg 1984—1985 

Visiting Professor, Visiting Scholar MIT, Cambridge, MA 1994—2001 

Link to this profile  http://www.faculty.uci.edu/profile.cfm?faculty_id=2054  
Last updated  02/05/2007  