Abstract
In quantum physics, the perturbation theory up to some finite order in the coupling constant contains a nonpositive-definite scalar product of physical wave functions or a nonunitary evolution of states. It cannot therefore be considered a consistent theory describing reality. This problem can be solved by modifying the scalar product of wave functions and the multiplication of dynamical variables. The obtained solutions can be used for an alternative description of quantum physical systems that agrees with experiment within the prescribed accuracy.
Similar content being viewed by others
References
C. M. Will, Living Rev. Relativ., 4, 2001-4 (2001); arXiv:gr-qc/0103036v1 (2001).
S. Deser, Class. Q. Grav., 4, L99–L105 (1987).
V. A. Kostelecký and R. Potting, Phys. Rev. D, 79, 065018 (2009); arXiv:0901.0662v1 [gr-qc] (2009).
R. Ph. Feynman, F. B. Morinigo, and W. G. Wagner, Feynman Lectures on Gravitation, Westview, Boulder, Colo. (1995).
A. G. Kurosh, Lectures in General Algebra (Intl. Ser. Monogr. Pure Appl. Math., Vol. 70), Pergamon, Oxford (1965).
Author information
Authors and Affiliations
Corresponding author
Additional information
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 181, No. 2, pp. 322–336, November, 2014.
Rights and permissions
About this article
Cite this article
Franke, V.A., Tsenderovskii, V.S. Alternative descriptions of physical systems based on perturbation theory. Theor Math Phys 181, 1405–1417 (2014). https://doi.org/10.1007/s11232-014-0221-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11232-014-0221-7