1999/04/27 by Ion I. Cotǎescu, Ion I. Cotaescu, Cotaescu, Ion I.
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Mathematical Physics (math-ph) #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/9904029
27 pages, Latex with amssym
openalex publication_date 1999/04/27 · arxiv created 2002/07/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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