Abstract
The concept of bra-vector is endowed with a precise mathematical meaning by taking a Hilbert-space H (whose elements are the ket-vectors) and embedding it into a larger bra-space L. The space L is constructed by fitting together all the different spaces with ``negative'' norm corresponding to equipping operators D in H. It is shown that the formal manipulations of Dirac's formalism become theorems on the resulting extended Hilbert space structure H⊂L. On L we define topologies and bra-adjoints of operators in H and investigate their properties. We show how these results can be used in deriving rigorous versions of the typical relations involving distorted waves in time-independent scattering theory. By applying this formalism to Fock space we obtain an extended Fock space framework suitable for the rigorous formulation of the concept of a field at a point in configuration or momentum space.
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