On the (1/2,1/2) Representation of the Lorentz Group and the Discrete CPT Symmetries

Abstract: This thesis derives the explicit form of the elements of the (1/2,1/2) representation of the Lorentz group, by actually performing a direct product of the chiral (1/2,0)- and (0,1/2)-representations. The Lorentz transformations of fourvectors are thereafter recovered from this direct-product representation, allowing the derivation of a transformation matrix between the fourvector- and direct product basis. This matrix is then used to explore the discrete C, P and T transformations in both bases.