Abstract
The procedure of passing from quantum statistical mechanics to the hydrodynamics previously developed by the author is now applied to the quantum field model ϕ4. For a certain class of external forces, the equations of many-body systems in quantum theory appear to be equivalent to the equations of nonlocal hydrodynamics. The hydrodynamic nonlocalities arising in constituent relations are expressed through the Green's functions for currents. Some properties of the nonlocal kernels, in particular, the conditions related to dissipation and T-invariance of the model ϕ4 (an analogue of Onsager's relations), are deduced from the general symmetry properties. In hydrodynamics, nonlocality allows causality and dissipativity to be consistently combined. The connection between the classical transport coefficients and the hydrodynamic kernels is established. An algorithm for calculating constituent relations by perturbation theory, using the technique of temperature Green's functions, is described.
Similar content being viewed by others
References
D. N. Zubarev,Non-Equilibrium Statistical Thermodynamics [in Russian], Nauka, Moscow (1971).
A. I. Akhiezer and S. B. Peletminski,Methods of Statistical Physics [in Russian], Nauka, Moscow (1977).
W. A. Hiscock and L. Lindblom,Phys. Rev. D,31, No. 4, 725–733 (1985).
B. Carter,Lect. Notes Math.,1385, 1–64 (1989).
W. Israel,Lect. Notes Math.,1385, 152–210 (1989).
O. Yu. Dinariev,Dokl. Akad. Nauk SSSR,301, 1095–1097 (1988).
O. Yu. Dinariev,Prikl. Mat. Mekh.,56, 250–259 (1992).
O. Yu. Dinariev,Izv. Vyssh. Uchebn. Zaved., Fiz., No. 5, 13–18 (1993).
O. Yu. Dinariev,Zh. Eksp. Teor. Fiz.,106, 161–171 (1994).
O. Yu. Dinariev,Zh. Eksp. Teor. Fiz.,107, 1877–1894 (1995).
O. Yu. Dinariev,Zh. Eks. Teor. Fiz.,107, 1573–1586 (1995).
A. D. Linde,Elementary Particle Physics and Inflation Cosmology [in Russian], Nauka, Moscow (1990).
Yu. S. Gangus, A. V. Prozorkevich, and S. A. Smolyanski,Teor. Mat. Fiz.,35, 68–75 (1978).
A. Hosoya, M. Sakagami, and M. Takao,Ann. Phys.,154, No. 1, 229–252 (1984).
G. Emch,Algebraic Methods in Statistical Mechanics and Quantum Field Theory [Russian translation], Mir. Moscow (1976).
N. N. Bogoliubov, A. A. Logunov, A. I. Oksak, and I. T. Todorov,General Principles of Quantum Field Theory [in Russian], Nauka, Moscow (1987).
A. A. Abrikosov, L. P. Gor'kov, and I. E. Dzyaloshinski,Methods of Quantum Field Theory in Statistical Physics [in Russian], Fizmatgiz, Moscow (1987).
L. D. Landau and E. M. Lifshitz,Theoretical Physics [in Russian], Vol. 9,Statistical Physics. Part 2.The Theory of Condensed States, Nauka, Moscow (1978).
O. Yu. Dinariev,Dokl. Akad. Nauk SSSR,309, 615–618 (1989).
L. D. Landau and E. M. Lifshitz,Theoretical Physics [in Russian], Vol. 6,Hydrodynamics, Nauka, Moscow (1986).
C. Eckart,Phys. Rev.,58, No. 10, 919–924 (1940).
U. Kraemmer, M. Kreuzer, A. Rebhan, and H. Schulz,Lect. Notes Phys.,361, 285–295 (1990).
Author information
Authors and Affiliations
Additional information
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 108, No. 1, pp. 50–68, July, 1996.
Rights and permissions
About this article
Cite this article
Dinariev, O.Y. Nonlocal hydrodynamics in the quantum field modelϕ 4 . Theor Math Phys 108, 889–903 (1996). https://doi.org/10.1007/BF02070515
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02070515