Joseph E. Johnson
Distinguished Professor Emeritus
PSC 405Physics and Astronomy
University of South Carolina
Columbia, South Carolina 29208
(803) 777-6431
Education
- PhD State University of New York at Stony Brook (Theoretical Physics)
- MS State University of Iowa (Theoretical Physics)
Research Interests
One of the most fundamental problems which emerges in relativistic quantum mechanics is to understand the Lie algebraic structures which are formed with different sets of primary observables. These sets of observables can form discrete groups like the inversions and charge conjugation or they may generate continuous Lie groups such as the Lorentz, Poincare and internal symmetry groups. These continuous groups in turn may be exact or approximate symmetry groups and pertain to relativistic quantum, or even classical mechanics. Recently I have been investigating Lie groups that contain transformations connected with classical nonrelativistic systems, such as Markov-type Lie groups, and studying their application to processes of diffusion and information theory. Such groups can be understood by considering alternative decompositions of the (homogeneous and inhomogeneous) general linear group GL(n,R). I am also working on the use of new data objects in computational problems.
Selected Publications
- Position Operators & Proper Time in Relativistic Quantum Mechanics, Phys. Rev. Vol 181, No 5 1755-1764 May 1969
- Proper Time Quantum Mechanics II, Phys. Rev. D Vol 3, No 8, 1735-1747 April 1971 1755-1764 May 1969
- Remark on the Isospin Mass Differences, Phys. Rev. D Vol 3, No 11, 2648- 2651, June 1, 1971
- Exact Diagonalization of the Dirac Hamiltonian in an External Field, Phys Rev D, Vol 10, No 8, 2421-2427 October 1974
- Markov-Type Lie Groups in GL(n,R) J. Math Phys. 26 (2) 252-257 February 1985