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 TMF, 1977, Volume 33, Number 1, Pages 17–31 (Mi tmf3201)

Uniformization method in the theory of Nonlinear Hamiltonian systems of Vlasov and Hartree type

V. P. Belavkin, V. P. Maslov

Abstract: Possibilities of obtaining the approximate solutions to the equations of the Hartree type from the known solutions of the uniformized linear equations are investigated. Nonlinear hamiltonian systems described by abstract equations of the Vlassov and Hartree type are considered by means of algebraic methods. New notion of the “unif ormization” is introduced which represents the generalization of the second quantization method for arbitrary Hamiltonian (Lie–Jordan) algebras, in particular, for operator algebras in indefinite spaces. Functional calculus of uniformized observables is developed, extending and unifying the calculus of generating functionals of commuting; and anticommuting variables for even operators.

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English version:
Theoretical and Mathematical Physics, 1977, 33:1, 852–862

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Citation: V. P. Belavkin, V. P. Maslov, “Uniformization method in the theory of Nonlinear Hamiltonian systems of Vlasov and Hartree type”, TMF, 33:1 (1977), 17–31; Theoret. and Math. Phys., 33:1 (1977), 852–862

Citation in format AMSBIB
\Bibitem{BelMas77} \by V.~P.~Belavkin, V.~P.~Maslov \paper Uniformization method in the theory of Nonlinear Hamiltonian systems of Vlasov and Hartree type \jour TMF \yr 1977 \vol 33 \issue 1 \pages 17--31 \mathnet{http://mi.mathnet.ru/tmf3201} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=478881} \transl \jour Theoret. and Math. Phys. \yr 1977 \vol 33 \issue 1 \pages 852--862 \crossref{https://doi.org/10.1007/BF01039008} 

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This publication is cited in the following articles:
1. V. P. Belavkin, V. P. Maslov, S. È. Tariverdiev, “Asymptotic dynamics of a system of a large number of particles described by the Kolmogorov–Feller equations”, Theoret. and Math. Phys., 49 (1981), 1043–1049
2. V. I. Gerasimenko, “Dynamical equations of quantum-classical systems”, Theoret. and Math. Phys., 50:1 (1982), 49–55
3. V. P. Maslov, A. M. Chebotarev, “On random fields corresponding to the BBGKY, Vlasov, and Boltzmann hierarchies”, Theoret. and Math. Phys., 54:1 (1983), 48–55
4. V. P. Maslov, O. Yu. Shvedov, “Asymptotics of a solution of an $N$-partial Liouville equation for large $N$ and refutation of the chaos hypothesis for density functions”, Math. Notes, 56:2 (1994), 872–874
5. V. P. Maslov, O. Yu. Shvedov, “Complex germ method in the Fock space. II. Asymptotics, corresponding to finite-dimensional isotropic manifolds”, Theoret. and Math. Phys., 104:3 (1995), 1141–1161
6. Maslov, VP, “Large-N expansion as a semiclassical approximation to the third-quantized theory”, Physical Review D, 6010:10 (1999), 105012
7. Maslov V.P., Shvedov O.Y., “Large-N expansion as a semiclassical approximation to the third-quantized theory”, Physical Review D, 60:10 (1999), 105012
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