<<
CHAPTER 2
Representations of the Lorentz and Poincare Groups and Transformation Properties of Physical Quantities
At the very outset, it is pertinent to mention that finite dimensional irreducible representations (IRRs) of both these groups are not unitary and all unitary representations are infinite dimensional since the groups are non-compact.
2.1 UNITARY REPRESENTATIONS OF THE LORENTZ GROUP (WIGNER, 1939; GEL'FAND, 1963; NAIMARK, 1964; OHNUKI, 1976; TUNG, 1984)
2.1.1 Reduction of Representations and Relabelling of Basis The Lie algebra for the proper Lorentz group is given by JJμλσv , = iejJ σvvg μλ J λg μσ J μλg v σ+ J μσg v λ (1) or equivalently by