Geodesic
Complex time transformation pecularities for wave function collapse description using quntum path integrals
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 137 (2014) no. 4, pp. 170-177 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A 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.
Keywords: wave function collapse, path integral, Wiener measure, complex time, Wick rotation. 
@article{VSGTU_2014_137_4_a14,
     author = {N. V. Meleshko and A. Yu. Samarin},
     title = {Complex time transformation pecularities for wave function collapse description using quntum path integrals},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {170--177},
     year = {2014},
     volume = {137},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2014_137_4_a14/}
}
TY  - JOUR
AU  - N. V. Meleshko
AU  - A. Yu. Samarin
TI  - Complex time transformation pecularities for wave function collapse description using quntum path integrals
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2014
SP  - 170
EP  - 177
VL  - 137
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2014_137_4_a14/
LA  - ru
ID  - VSGTU_2014_137_4_a14
ER  - 
%0 Journal Article
%A N. V. Meleshko
%A A. Yu. Samarin
%T Complex time transformation pecularities for wave function collapse description using quntum path integrals
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2014
%P 170-177
%V 137
%N 4
%U http://geodesic.mathdoc.fr/item/VSGTU_2014_137_4_a14/
%G ru
%F VSGTU_2014_137_4_a14
N. V. Meleshko; A. Yu. Samarin. Complex time transformation pecularities for wave function collapse description using quntum path integrals. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 137 (2014) no. 4, pp. 170-177. http://geodesic.mathdoc.fr/item/VSGTU_2014_137_4_a14/

[1] von Neumann J., Mathematical foundations of quantum mechanics, Investigations in Physics, 2, Princeton, Princeton Univ. Press, 1955, xii+445 pp. | MR | Zbl

[2] Bell J., “Against ‘measurement’”, Physics World, 1990, August, 33–40

[3] Everett H., ““Relative State” Formulation of Quantum Mechanics”, Rev. Mod. Phys., 29:3 (1957), 454–462 | DOI | MR

[4] Mensky M. B., “Quantum measurements, the phenomenon of life, and time arrow: three great problems of physics (in Ginzburg's terminology) and their interrelation”, Phys. Usp., 50:4 (2007), 397–407 | DOI | DOI | MR

[5] Samarin A. Yu., “Description of discrete spectrum states transition processes”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2009, no. 2(19), 226–230 (In Russian) | DOI

[6] Samarin A. Yu., “Natural space of the micro-object”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2011, no. 3(24), 117–128 (In Russian) | DOI

[7] Feynman R. P., “Space-time approach to non-relativistic quantum mechanics”, Rev. Mod. Phys., 20:2 (1948), 367–387 ; Feynman R. P., “Space-time approach to non-relativistic quantum mechanics”, Feynman's Thesis — A New Approach to Quantum Theory, World Scientific Publ., Singapore, 2005, 71–109 | DOI | MR | Zbl | DOI

[8] Feynman R. P., Hibbs A. R., Quantum Mechanics and Path Integrals, McGraw-Hill, New York, 1965, 371+xii pp. | MR | Zbl

[9] Samarin A. Yu., “Quantum Particle Motion in Physical Space”, Advanced Studies in Theoretical Physics, 8:1 (2014), 27–34, arXiv: [quant-ph] 1407.3559 | DOI

[10] Samarin A. Yu., “Space localization of the quantum particle”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2013, no. 1(30), 387–397 (In Russian) | DOI

[11] Vasiliev A. N., Functional Methods in Quantum Field Theory and Statistical Physics, Gordon and Breach Science Publ., Amsterdam, 1998, xiv+312 pp. | MR | Zbl

[12] Popov V. N., Kontinual'nye integraly v kvantovoi teorii polia i statisticheskoi fizike [Path Integrals in Quantum Field Theory and Statistical Physics], Atomizdat, Moscow, 1978, 256 pp. (In Russian) | MR

[13] Faddeev L. D., Slavnov A. A., Gauge fields: introduction to quantum theory, Frontiers in Physics, 50, Benjamin/Cummings, Advanced Book Program, Reading, Mass., 1980, xiii+232 pp. | MR | Zbl

[14] Zinn Justin J., Path Integrals in Quantum Mechanics, Oxford University Press, Oxford, 2004, 320+xiv pp. | DOI | MR

[15] Samarin A. Yu., Macroscopic Body Motion in Terms of Quantum Evolution, 2004, 5 pp., arXiv: [quant-ph] 1408.0340

[16] Kac M., Probability and related topics in physical sciences, Lectures in Applied Mathematics, I, Interscience Publ., London, New York, 1959, xiii+266 pp. | MR