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Parity transformation of the coordinates |
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Transformation of the generators A and B of the Lorentz group |
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Therefore under the parity transformation the representations (j1j2) and (j2j1) of the Lorentz group transform into each other |
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Irreducible representation D(j1,j2) of the general Lorentz group can then be made as a direct sum (j1j2)⊕(j2j1) |
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For the important spin ½ field the Lorentz transformation is | ( φχ )' = [ d0 0(d+)-1 ] ( φχ ) |
Scalar, S= |
Pseudoscalar, P= |
Four-vector, Vi= |
Pseudo-vector, Ai= |
Antisymmetric tensor Tij =
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