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College of Arts & Sciences
Advanced Solutions Group

Dr. Joseph Johnson


Physics Dept., University of South Carolina
Columbia SC, 29208

Phone: 803.777.6431

Fax: 803.777.8833

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  • PhD State University of New York at Stony Brook (Theoretical Physics)
  • MS State University of Iowa (Theoretical Physics)
  • BA Vanderbilt University (Physics & Mathematics)

Professional Experience


  • Physics Department, University of South Carolina
  • Distinguished Professor Emeritus, & Distinguished Research Professor
  • Distinguished Professor of Physics,Univ. of South Carolina
  • Associate Chair, Department of Physics, Univ. of South Carolina
  • Associate Dean for Graduate Studies, College of Science and Math, USC
  • Associate Dean for Graduate Studies, College of Science and Math, USC
  • Associate Professor with Tenure at USC
  • Assitant Professor of Physics, USC
  • Instructor, Physics Department; State University of Ny at Stony Brook


Core Research

  1. Position Operators & Proper Time in Relativistic Quantum Mechanics, Phys. Rev. Vol 181, No 5 1755-1764 May 1969
  2. Proper Time Quantum Mechanics II,  Phys. Rev. D Vol 3, No 8, 1735-1747 April 1971 1755-1764 May 1969
  3. Remark on the Isospin Mass Differences, Phys. Rev. D Vol 3, No 11, 2648-2651, June 1, 1971
  4. Exact Diagonalization of the Dirac Hamiltonian in an External Field, Phys Rev D, Vol 10, No 8, 2421-2427 October 1974
  5. Markov-Type Lie Groups in GL(n,R) J. Math Phys. 26 (2) 252-257 February 1985
  6. Networks, Markov Lie Monoids, and Generalized Entropy, Computer Networks Security – Third International Workshop on Mathematical Methods, Models, and Architectures for Computer Network Security, St. Petersburg, Russia, September 2005, Proceedings, 129-135

Other Areas

  1. Income Elasticity of the Residential Demand for Electricity, Ronald P Wilder, Joseph E. Johnson, & R. Glenn Rhyne, The Journal of Energy & Development Vol 16, No 1, 1-13 Autumn 1990
  2. Risk Factors for Traumatic Physical Injury During Sexual Assaults for Male and Female Victims, Ann L Coker, Lucille G Walls, & Joseph E. Johnson, Journal of Interpersonal Violence Vol 12, No 5, 605-620 October 1998

Patents & Copyrights

  • 1986 – Three registered copyrights on UNITS Metadata Management Software
  • 2006 – US Patent: Algorithm for the Management of Numerical Uncertainty
  • 2008 – Patent Pending: An Alternative Form of Game Theory with Expert Consensus
  • 2012 – US Patent: Entropy Metrics Algorithms using Markov Monoids
  • 2013 – Provisional Patent(in process): Integrated Standard for Units, Uncertainty, and Metadata

Dr. Johnson's primary research interest is theoretical physics with specialization in the foundations of relativistic quantum theory using a foundation with Lie Algebras where his initial work developed a new formulation of relativistic position operators and a relativistically covariant formulation of the Foldy-Wouthousen Transformation for charged spin ½ particles. Later he found a new method of decomposing the Lie group and algebra for the most general linear nxn transformations into a n-dimensional scaling algebra and an n(n-1)-dimensional Markov type Lie algebra. This latter algebra, when restricted using a particular Lie basis, generates all possible continuous Markov transformations (a Markov Monoid (MM)). This MM is instrumental in the study of entropy, information theory, and diffusion. One of his most important discoveries was that the MM Lie algebra is exactly isomorphic to all possible networks. This now allows the power of Lie groups and algebras to link to the theory of Markov transformations, and likewise to the full theory of networks and their classifications.

His USC R&D team (the Advanced Solutions Group – developed advanced software systems and he was the sole PI for over 120 grants for $14M between 1992 to 2012 to USC making him one of the highest funded faculty at USC. His funding by DARPA with $2.4M in 2004-2007 allowed him to make the breakthroughs that use Markov entropy metrics for analyzing networks. Currently his work concentrates on (1) the proposed numerical metadata system , (2) the QRECT classroom system ( that uses advanced expert algorithms for self-correcting systems, and the mathematical foundations of networks ( ). The QRECT cloud software allows all students use internet devices (like iPhones) to respond to questions in general form during class and is seen on the instructor's iPad. (3) He continues his research in integrating information theory, Markov theory, Lie Algebras, measurement theory, metanumber structures, and related concepts.

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