International Journal of Theoretical Physics

, Volume 11, Issue 5, pp 305–308 | Cite as

Square-roots, internal symmetries, and fermion field quantization

  • Gerald Rosen


It is observed that the complex square-root of the hermitian matrix σμpμ associated with a physical four-momentum admits Lorentz-independent unitary transformations that may be related to the internal symmetries of hadrons. An operator-valued square-root of the Hilbert space inner product in relativistic one-electron theory brings in fermion field quantization conditions as a direct concomitant of its linearity and hermicity properties.


Hilbert Space Field Theory Elementary Particle Quantum Field Theory Quantization Condition 
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  1. Perlis, S. (1952).Theory of Matrices, p. 203. Addison-Wesley, Cambridge, Massachusetts.Google Scholar
  2. Rosen, G. (1969).Formulations of Classical and Quantum Dynamical Theory, Appendix A. Academic Press, New York.Google Scholar
  3. Schweber, S. S. (1962).Introduction to Relativistic Quantum Field Theory. Harper and Row, New York.Google Scholar

Copyright information

© Plenum Publishing Company Limited 1974

Authors and Affiliations

  • Gerald Rosen
    • 1
  1. 1.Drexel UniversityPhiladelphia

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