Gauge-independent canonical formulation of relativistic plasma theory

Bialynicki‐Birula, Iwo; Hubbard, J. C.; Turski, Łukasz A.

doi:10.1016/0378-4371(84)90189-4

Cited by 60 publications

(41 citation statements)

References 15 publications

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“…Several other applications, notably the relativistic charged particle systems which can also be formulated within the metriplectic scenario have been discussed previously [17,18]. The quantum applications are of particular interest in view of some similarity between the metriplectic approach and the Lindblads construction [19] -the standard tool in dissipative quantum system analysis.…”

Section: Final Commentsmentioning

confidence: 99%

On the Dirac approach to constrained dissipative dynamics

Nguyen

Turski

2001

J. Phys. A: Math. Gen.

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In this paper we propose a novel algebraic and geometric description for the dissipative dynamics. Our formulation bears some similarity with the Poisson structure for non-dissipative systems. We develop a canonical description for constrained dissipative systems through an extension of the Dirac brackets concept, and we present a new formula for calculating Dirac brackets. This formula is particularly useful in description of dynamical systems with many second-class constraints. After presenting necessary formal background we illustrate our method on several examples taken from particle dynamics, continuum media physics and wave mechanics.

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Section: Final Commentsmentioning

confidence: 99%

On the Dirac approach to constrained dissipative dynamics

Nguyen

Turski

2001

J. Phys. A: Math. Gen.

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“…First let us recall that the interaction between electromagnetic fields and charged particles (of normalized mass m = 1 and charge e = 1) is given as the sum of the kinetic energy of the particles plus the energy of the field [12,13,14]:…”

Section: Hamiltonian Formulation Of Vlasov-maxwell Equationsmentioning

confidence: 99%

Hamiltonian description of a self-consistent interaction between charged particles and electromagnetic waves

2008

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The Hamiltonian description of the self-consistent interaction between an electromagnetic planewave and a co-propagating beam of charged particles is considered. We show how the motion can be reduced to a one-dimensional Hamiltonian model (in a canonical setting) from the Vlasov-MaxwellPoisson brackets. The reduction to this paradigmatic Hamiltonian model is performed using a Lie algebraic formalism which allows us to remain Hamiltonian at each step of the derivation.

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“…It is well-known that the Vlasov equation possesses an infinite dimensional Hamiltonian structure [1][2][3][4]. An interesting feature of this structure is that the natural variable, the phase space density, constitutes noncanonical coordinates, and as a result the Poisson bracket has a noncanonical form.…”

Section: Introductionmentioning

confidence: 99%