De Donder-Weyl equations and multisymplectic geometry

Paufler, Cornelius; Römer, Hartmann

doi:10.1016/s0034-4877(02)80030-1

Cited by 18 publications

(23 citation statements)

References 13 publications

(13 reference statements)

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“…e.g. see references [3,[53][54][55][56][57]. (Here, we mention in particular the comprehensive Gimmsy papers [53] which addressed the relation of multisymplectic geometry with the standard canonical approach to field theory that is generally considered for quantization.)…”

Section: Generalitiesmentioning

confidence: 99%

Covariant canonical formulations of classical field theories

Gieres¹

2021

Preprint

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who established many original and profound results in pure mathematics which found important applications in physics to which he also contributed substantially by his work and his action. By his wonderful lectures he conveyed his broad knowledge while highlighting the essential points and casting the physical concepts in their appropriate mathematical setting. An outstanding, undogmatic and open-minded mathematician of great simplicity and generosity left us while leaving a lasting impression on all those who had the chance to meet him.

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Section: Generalitiesmentioning

confidence: 99%

Covariant canonical formulations of classical field theories

Gieres¹

2021

Preprint

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“…A general description of the de-Donder Weyl equations and multi-symplectic geometry has been given for example by Paufler and Römer (2002), who use the language of fiber bundles. We present an elementary derivation of the general form of the de Donder-Weyl Hamiltonian equations below.…”

Section: A the De Donder-weyl Formulationmentioning

confidence: 99%

Multi-symplectic, Lagrangian, one-dimensional gas dynamics

Webb

2015

Journal of Mathematical Physics

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The equations of Lagrangian, ideal, one-dimensional (1D), compressible gas dynamics are written in a multi-symplectic form using the Lagrangian mass coordinate m and time t as independent variables, and in which the Eulerian position of the fluid element x = x(m, t) is one of the dependent variables. This approach differs from the Eulerian, multi-symplectic approach using Clebsch variables. Lagrangian constraints are used to specify equations for x m , x t and S t consistent with the Lagrangian map, where S is the entropy of the gas. We require S t = 0 corresponding to advection of

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“…In this section, we consider the following first-order PDE, known as DW HamiltonJacobi equation [11,20] …”

Section: Dw Hamilton-jacobi Equationmentioning

confidence: 99%