Quantum Measure as a Necessary Ingredient in Quantum Gravity and Modified Gravities
Dzhunushaliev V. Folomeev V.
December 2024Pleiades Publishing
Gravitation and Cosmology
2024#30Issue 4401 - 407 pp.
Abstract: We suggest commutation relations for a quantum measure. In one version of these relations, the right-hand side takes account of the presence of curvature of space; in the simplest case, this yields the action of general relativity. We consider the cases of quantization of the measure on spaces of constant curvature and show that in this case the commutation relations for the quantum measure are analogues of commutation relations in loop quantum gravity. It is assumed that, in contrast to loop quantum gravity, a triangulation of space is a necessary trick for quantizing such a nonlocal quantity as a measure; and at that, the space remains a smooth manifold. We consider the self-consistent problem of interaction of the quantum measure and classical gravitation. It is shown that this inevitably leads to the emergence of modified gravities. Also, we consider the problem of defining the Euler–Lagrange equations for a matter field in the background of a space endowed with quantum measure.
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Department of Theoretical and Nuclear Physics, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Academician J. Jeenbaev Institute of Physics of the NAS of the Kyrgyz Republic, 265a, Chui street, Bishkek, 720071, Kyrgyzstan
International Laboratory for Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), Tomsk, 634050, Russian Federation
Department of Theoretical and Nuclear Physics
Academician J. Jeenbaev Institute of Physics of the NAS of the Kyrgyz Republic
International Laboratory for Theoretical Cosmology
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026