On the use of projectors for Hamiltonian systems and their relationship with Dirac brackets

被引：25

作者：

Chandre, C. ^{[1
]}

de Guillebon, L. ^{[1
]}

Back, A. ^{[1
]}

Tassi, E. ^{[1
]}

Morrison, P. J. ^{[2
]}

机构：

[1] Aix Marseille Univ, CNRS, Ctr Phys Theor, F-13288 Marseille 09, France

[2] Univ Texas Austin, Dept Phys, Austin, TX 78712 USA

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2013年 / 46卷 / 12期

关键词：

MAXWELL-VLASOV EQUATIONS; FLUID;

D O I：

10.1088/1751-8113/46/12/125203

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The role of projectors associated with Poisson brackets of constrained Hamiltonian systems is analyzed. Projectors act in two instances in a bracket: in the explicit dependence on the variables and in the computation of the functional derivatives. The role of these projectors is investigated by using Dirac's theory of constrained Hamiltonian systems. Results are illustrated by three examples taken from plasma physics: magnetohydrodynamics, the Vlasov-Maxwell system, and the linear two-species Vlasov system with quasineutrality.

引用

页数：14

共 11 条

[1] GAUGE-INDEPENDENT CANONICAL FORMULATION OF RELATIVISTIC PLASMA THEORY [J].

BIALYNICKIBIRULA, I ;

HUBBARD, JC ;

TURSKI, LA .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 1984, 128 (03) :509-519

[2]

Hanson A. J., 1976, Constrained Hamiltonian Systems

[3] THE HAMILTONIAN-STRUCTURE OF THE MAXWELL-VLASOV EQUATIONS [J].

MARSDEN, JE ;

WEINSTEIN, A .

PHYSICA D, 1982, 4 (03) :394-406

[4] A general theory for gauge-free lifting [J].

Morrison, P. J. .

PHYSICS OF PLASMAS, 2013, 20 (01)

[5]

MORRISON PJ, 1982, PHYS REV LETT, V48, P569, DOI 10.1103/PhysRevLett.48.569

[6]

MORRISON PJ, 1982, AIP CONF PROC, P13

[7] Hamiltonian description of the ideal fluid [J].

Morrison, PJ .

REVIEWS OF MODERN PHYSICS, 1998, 70 (02) :467-521

[8] THE MAXWELL-VLASOV EQUATIONS AS A CONTINUOUS HAMILTONIAN SYSTEM [J].

MORRISON, PJ .

PHYSICS LETTERS A, 1980, 80 (5-6) :383-386

[9] Canonical description of incompressible fluid: Dirac brackets approach [J].

Nguyen, S ;

Turski, LA .

PHYSICA A, 1999, 272 (1-2) :48-55

[10] Examples of the Dirac approach to dynamics of systems with constraints [J].

Nguyen, S ;

Turski, LA .

PHYSICA A, 2001, 290 (3-4) :431-444

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