Generalized "bra-ket" formalism

Details Generalized "bra-ket" formalism Generalized "bra-ket" formalism

1999-04-27

arxiv.org/abs/math-ph/9904029v2

Physics

Mathematical Physics

27 pages, Latex with amssym

Scientific paper

The Dirac's bra-ket formalism is generalized to finite-dimensional vector spaces with indefinite metric in a simple mathematical context similar to thatof the theory of general tensors where, in addition, scalar products are introduced with the help of a metric operator. The specific calculation rules are given 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 $SL(2,\Comp)$ group with invariant scalar products. Pacs: 02.10.Sp, 02.20.Qs

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