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  • In this paper, a general Hamiltonian theory for Lagrangian systems on fibred manifolds is proposed. The concept of a Lepagean (n+1)-form is defined, generalizing Krupka's concept of a Lepagean n-form. Lepagean (n+1)-forms are used to study Lagrangian andHamiltonian systems. Innovations and new results concern the following: a Lagrangian system is considered as an equivalence class of local Lagrangians; a Hamiltonian system is associated with an Euler-Lagrange form (not with a particular Lagrangian); Hamilton equations are based upon a Lepagean (n+1)-form, and cover Hamilton-De Donder equations as a special case. First-order Hamiltonian systems, namely those carying higher-degree contact components of the corresponding Lepagean forms, are studied in detail. The presented geometric setting leads to a new understanding of the concepts of regularity and Legendre transformation in the calculus of variations, relating them directly to the properties of the arising exterior differential systems.
  • In this paper, a general Hamiltonian theory for Lagrangian systems on fibred manifolds is proposed. The concept of a Lepagean (n+1)-form is defined, generalizing Krupka's concept of a Lepagean n-form. Lepagean (n+1)-forms are used to study Lagrangian andHamiltonian systems. Innovations and new results concern the following: a Lagrangian system is considered as an equivalence class of local Lagrangians; a Hamiltonian system is associated with an Euler-Lagrange form (not with a particular Lagrangian); Hamilton equations are based upon a Lepagean (n+1)-form, and cover Hamilton-De Donder equations as a special case. First-order Hamiltonian systems, namely those carying higher-degree contact components of the corresponding Lepagean forms, are studied in detail. The presented geometric setting leads to a new understanding of the concepts of regularity and Legendre transformation in the calculus of variations, relating them directly to the properties of the arising exterior differential systems. (en)
Title
  • Hamiltonian field theory
  • Hamiltonian field theory (en)
skos:prefLabel
  • Hamiltonian field theory
  • Hamiltonian field theory (en)
skos:notation
  • RIV/47813059:19610/02:00000084!RIV/2003/GA0/196103/N
http://linked.open.../vavai/riv/strany
  • 93;132
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/00/0724), Z(MSM 192400002)
http://linked.open...iv/cisloPeriodika
  • 2
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 647387
http://linked.open...ai/riv/idVysledku
  • RIV/47813059:19610/02:00000084
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Lagrangian; Poincaré-Cartan form; Lepagean n-form; Lepagean (n+1)-form; Hamilton extremal;Hamilton equations; Hamilton-De Donder equations; Regularity; Legendre transformation (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • IT - Italská republika
http://linked.open...ontrolniKodProRIV
  • [2C66066AC44D]
http://linked.open...i/riv/nazevZdroje
  • Journal of Geometry and Physics
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...ocetUcastnikuAkce
http://linked.open...nichUcastnikuAkce
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 43
http://linked.open...iv/tvurceVysledku
  • Krupková, Olga
http://linked.open...n/vavai/riv/zamer
issn
  • 0393-0440
number of pages
http://localhost/t...ganizacniJednotka
  • 19610
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