Using methods analogous to those introduced by Gel’fand et al. [Representations of the rotation and Lorentz Groups and Their Applications (Pergamon, New York, 1963)] for the Lorentz group the matrix elements for the representations of the Lie algebra of the Euclidean group in three dimensions E(3) are explicitly derived. These results are then used to construct invariant equations with respect to this group and to show, in particular, that the nonrelativistic analog to the Dirac equation is not unique.
REFERENCES
1.
J.‐M Levy‐Leblond, Galilei Group and Galilean Invariance in Group Theory and its Applications, edited by E. M. Loebl (Academic, New York, 1971), Vol. II;
this review article contains an extensive list of references;
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I. M. Gel’fand, R. A. Minlos, and Z. Ya. Shapiro, Representations of the Rotation and Lorentz Groups and Their Applications (Pergamon, New York, 1963).
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© 1987 American Institute of Physics.
1987
American Institute of Physics
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