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<p>The widespread bra-ket formalism offers valuable tools for conducting representation-free considerations in quantum theory. However, it is not without its drawbacks. In this work, we discuss these drawbacks in detail and subsequently construct a new representation-free scheme. Similar to the bra-ket formalism, the present scheme provides essential means to facilitate representation-free considerations. At the same time, it is entirely free from the drawbacks of the bra-ket formalism. Unlike the dual-space bra-ket formalism, the present scheme allows both one-space and dual-space interpretations, which is a beneficial feature. The constructed universal scheme is very well-suited for performing representation-free practical calculations.</p>

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On the representation-free formalism in quantum theory

  • 期刊论文

  • 发表日期：

    2025年9月20日

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  • V. D. Efros

摘要

The widespread bra-ket formalism offers valuable tools for conducting representation-free considerations in quantum theory. However, it is not without its drawbacks. In this work, we discuss these drawbacks in detail and subsequently construct a new representation-free scheme. Similar to the bra-ket formalism, the present scheme provides essential means to facilitate representation-free considerations. At the same time, it is entirely free from the drawbacks of the bra-ket formalism. Unlike the dual-space bra-ket formalism, the present scheme allows both one-space and dual-space interpretations, which is a beneficial feature. The constructed universal scheme is very well-suited for performing representation-free practical calculations.