Generalized Dirac Formalism

The usual bra-ket formalism is generalized to finite-dimensional vector spaces with indefinite metric in a simple mathematical context similar to that of the theory of general tensors where, in addition, scalar products are introduced with the help of a metric operator. The specific calculation rules are presented with all their details in a suitable intuitive notation. It is shown that the proposed bra-ket calculus is appropriate for the general theory of basis transformations and finite-dimensional representations of the symmetry groups of the metric operators. The presented application is the theory of finite-dimensional representations of the SL(2, C) group with invariant scalar products. Pacs: 02.10.Sp, 02.20.Qs