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Pauli Matrices, Spinors, Dirac Matrices, and Dirac Bispinors

  • Anadijiban Das
Chapter
  • 641 Downloads
Part of the Universitext book series (UTX)

Abstract

A rotation in the Euclidean plane can be characterized by the following matrix equation:
$$ \left[ {\begin{array}{*{20}c} {\hat x^1 } \\ {\hat x^2 } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {cos\varphi } \\ { - \sin \varphi } \\ \end{array} \begin{array}{*{20}c} {\sin \varphi } \\ {\cos \varphi } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {x^1 } \\ {x^2 } \\ \end{array} } \right], $$
where φ ∈ ( - π, π) and x1, x2 are Cartesian coordinates.

Keywords

Lorentz Transformation Pauli Matrice Hermitian Matrix Pauli Matrix Dirac Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    W. L. Bade and H. Jehle, Rev. Mod. Phys. 25 (1953), 714–728. [pp. 104, 112, 115]MathSciNetADSzbMATHCrossRefGoogle Scholar
  2. 2.
    E. M. Corson, Introduction to tensors, spinors, and relativistic wave-equations, Blackie and Son, London, 1955. [pp. 112, 115, 121]Google Scholar
  3. 3.
    I. M. Gelfand, R. A. Milnos, and Z. Y. Shapiro, Representations of the rotation and Lorentz groups, and their applications, The MacMillan Co., New York, 1963. [pp. 102, 103, 235]Google Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Anadijiban Das
    • 1
  1. 1.Department of Mathematics and StatisticsSimon Fraser UniversityBurnabyCanada

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