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
