Abstract
A current density operator jμ (x) between oneparticle states is the simplest example of a covariant (in this case: vector) operator connecting two (in this case: reducible unitary) representations of the group SL(2,C). In these lectures we review first the representation theory of the group SL(2,C). This enables us to derive a decomposition theorem for covariant operators with heuristic arguments. By this theorem we can decompose any covariant operator into a direct integral of irreducible covariant operators, which are defined to connect two irreducible representations of SL(2,C). This formalism is then applied to several problems of physical interest.
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