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Formulation of quantum mechanics with dynamical time

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Abstract

We consider quantum mechanics for which the system time is one of generalized coordinates. The generalized Hamiltonian has an unbounded spectrum, which allows us to introduce a Hermitian time operator. In the proposed formulation of quantum mechanics, a system time and observer’s time are introduced. The Schrödinger equation in the system time either does not hold or holds only approximately. The wave function is assumed to be square integrable with respect to all coordinates, including the system time. In some limit, this formalism reproduces standard quantum mechanics and the corresponding measurement theory.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

    M. G. Ivanov

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  1. M. G. Ivanov
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Correspondence to M. G. Ivanov.

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Original Russian Text © M.G. Ivanov, 2014, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Vol. 285, pp. 154–165.

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Ivanov, M.G. Formulation of quantum mechanics with dynamical time. Proc. Steklov Inst. Math. 285, 145–156 (2014). https://doi.org/10.1134/S0081543814040117

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