Journal of Samara State Technical University, Ser. Physical and Mathematical SciencesJournal of Samara State Technical University, Ser. Physical and Mathematical Sciences1991-86152310-7081Samara State Technical University2077610.14498/vsgtu1352Research ArticleComplex time transformations peculiarities for wave function collapse description using quantum path integralsMeleshkoNatalia VSenior Lecturer, Dept. of General Physics and Physics of Oil and Gas Productionmeleshko1958@gmail.comSamarinAlexey Yu(Cand. Phys. & Math. Sci.; samarinay@yahoo.com; Corresponding Author), Associate Professor, Dept. of General Physics and Physics of Oil and Gas Productionsamarinay@yahoo.comSamara State Technical University1512201418417017718022020Copyright © 2014, Samara State Technical University2014A quantum path integral was transformed into the real form using a complex representation of the time. Such procedure gives the possibility to specify measures for the sets of the virtual paths in continual integrals determining amplitudes of quantum states transitions. The transition amplitude is a real function of the complex time modulus. Negative time values correspond to the reverse sequence of events. The quantum evolution description in form of the virtual paths mechanical motion does not depend on the sign of the time, due to the reversibility of the classical mechanics laws. This allows to consider the negative half of the imaginary axis of the time for the path integral measure determination. In this case this integral has the form of Wiener's integral having the well-known measure. As the wave function collapse is irreversible effect, the causal chain of events cannot be changed. Thus, to describe the collapse the transformation of quantum path integrals have to be performed in upper half plane of the complex time. It is shown that the Wiener measure for the real continual integral can be continued analytically on this actual range of the complex time. This allows to use the quantum path integral for any actual range of the complex time.wave function collapsepath integralWiener measurecomplex timeWick rotationколлапс волновой функцииинтеграл по траекторияминтегральная мера Винеракомплексное времяповорот Вика[von Neumann J. Mathematical foundations of quantum mechanics / Investigations in Physics. vol. 2. Princeton Univ. Press: Princeton, 1955. xii+445 pp.][Bell J. Against ‘measurement’ // Physics World, 1990. August. pp. 33-40][Everett H. “Relative State” Formulation of Quantum Mechanics // Rev. Mod. Phys., 1957. vol. 29, no. 3. pp. 454-462. doi: 10.1103/revmodphys.29.454.][Менский М. Б. Квантовые измерения, феномен жизни и стрела времени: связи между «тремя великими проблемами» (по терминологии В. Л. Гинзбурга) // УФН, 2007. Т. 177, № 4. С. 415-425. doi: 10.3367/UFNr.0177.200704j.0415.][Самарин А. Ю. Описание процесса перехода между состояниями дискретного спектра // Вестн. Сам. гос. техн. ун-та. Сер. Физ.-мат. науки, 2009. № 2(19). С. 226-230. doi: 10.14498/vsgtu721.][Самарин А. Ю. Естественное пространство микрообъекта // Вестн. Сам. гос. техн. ун-та. Сер. Физ.-мат. науки, 2011. № 3(24). С. 117-128. doi: 10.14498/vsgtu911.][Feynman R. P. Space-time approach to non-relativistic quantum mechanics // Rev. Mod. Phys., 1948. vol. 20, no. 2. pp. 367-387. doi: 10.1103/revmodphys.20.367][Feynman R. P. Space-time approach to non-relativistic quantum mechanics / Feynman's Thesis - A New Approach to Quantum Theory. Singapore: World Scientific Publ., 2005. pp. 71-109. doi: 10.1142/9789812567635_0002.][Feynman R. P., Hibbs A. R. Quantum Mechanics and Path Integrals. New York: McGrawHill, 1965. 371+xii pp.][Samarin A. Yu. Quantum Particle Motion in Physical Space // Advanced Studies in Theoretical Physics, 2014. vol. 8, no. 1. pp. 27-34, arXiv: 1407.3559 [quant-ph]. doi: 10.12988/astp.2014.311136.][Самарин А. Ю. Пространственная локализация квантовой частицы // Вестн. Сам. гос. техн. ун-та. Сер. Физ.-мат. науки, 2013. № 1(30). С. 387-397. doi: 10.14498/vsgtu1138.][Васильев А. Н. Функциональные методы в квантовой теории поля и статистики. Ленинград: ЛГУ, 1978. 295 с.][Попов В. Н. Континуальные интегралы в квантовой теории поля и статистической физике. М.: Атомиздат, 1978. 256 с.][Faddeev L. D., Slavnov A. A. Gauge fields: introduction to quantum theory / Frontiers in Physics. vol. 50. Reading, Mass.: Benjamin/Cummings, Advanced Book Program, 1980. xiii+232 pp.][Zinn Justin J. Path Integrals in Quantum Mechanics. Oxford: Oxford University Press, 2004. 320+xiv pp. doi: 10.1093/acprof:oso/9780198566748.001.0001.][Samarin A. Yu. Macroscopic Body Motion in Terms of Quantum Evolution, 2004. 5 pp., arXiv: 1408.0340 [quant-ph].][Kac M. Probability and related topics in physical sciences / Lectures in Applied Mathematics. vol. I. London, New York: Interscience Publ., 1959. xiii+266 pp.][Bell J. S. Against “measurement” // NATO ASI Series, 1990. vol. 226. pp. 17-31. doi: 10.1007/978-1-4684-8771-8_3]