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Special Considerations on the Lorentz Group
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4-spinor 4-vector algebra angular momentum antisymmetric arbitrary centrum Chapter commutation rules condition conjugate connection consider contact transformations contravariant coordinate system corresponding covariant defined denote density derivatives determined diagonal dimensions Dirac equation Duffin-Kemmer eigenvalues elements energy-momentum tensor equivalent essentially example factor field equations field variables Fierz follows formalism given half-integral spin Hamiltonian hence Hermitian higher-spin idempotents indices infinitesimal operators infinitesimal transformations integral spin irreducible repre irreducible representations Lagrangian linear linearly independent Lorentz group Lorentz invariance Lorentz transformation matrix meson non-zero obtain operators orthogonal group particles Pauli Peirce decomposition physical positive definite proper Lorentz group properties pseudoscalar pseudovector quantities quantized relation relativistic respectively rest system rest-mass ring rotation satisfy scalar second-order second-rank self-dual sentation Similarly simple space-like spin transformation spinor symmetric theorem tions total energy transforming according uA(k unitary values vector wave equation wave functions wave-equation zero