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An algebraic PT-symmetric quantum theory with a maximal mass

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Abstract

In this paper, we draw attention to the fact that the studies by V.G. Kadyshevsky devoted to the creation of the geometric quantum field theory with a fundamental mass have had great development recently, as regards a non-Hermitian algebraic approach to construction of the quantum theory. The central idea of such theories is to construct a new scalar product in which the average values of non-Hermitian Hamiltonians are real. Many studies in this field include both purely mathematical ones and those containing the discussion of experimental results. We consider the development of an algebraic relativistic pseudo-Hermitian quantum theory with a maximal mass and discuss its experimentally important corollaries.

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Authors and Affiliations

  1. Plekhanov Russian University of Economics, Faculty of Mathematical Economics and Informatics, Stremyannyi per. 36, Moscow, 117997, Russia

    V. N. Rodionov

  2. Faculty of Physics, Moscow State University, Vorob’evy gory 1, Moscow, 119991, Russia

    G. A. Kravtsova

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  1. V. N. Rodionov
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  2. G. A. Kravtsova
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Original Russian Text © V.N. Rodionov, G.A. Kravtsova, 2016, published in Fizika Elementarnykh Chastits i Atomnogo Yadra, 2016, Vol. 47, No. 2.

In blessed memory of Vladimir Georgievich Kadyshevsky

“The stone which the builders rejected has become the head of the corner” (Psalm 117:22-23).

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Rodionov, V.N., Kravtsova, G.A. An algebraic PT-symmetric quantum theory with a maximal mass. Phys. Part. Nuclei 47, 135–156 (2016). https://doi.org/10.1134/S1063779616020052

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