On the representation-free formalism in quantum mechanics

Abstract: The widespread bra-ket formalism provides efficient means to carry out representation-free considerations in quantum theory. At the same time, drawbacks are inherent in it. We discuss these drawbacks in detail, and then, construct a new representation-free scheme. The present scheme provides efficient means to facilitate representation-free considerations, similar to all those offered by the bra-ket scheme but has none of the drawbacks of the bra-ket scheme. And, in contrast to the bra-ket formalism, the present scheme allows both the one-space and dual-space interpretations, which is a helpful feature. The constructed scheme is advantageous for performing representation-free practical calculations.