Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   

Поиск по указателям

Kastrup H.A. — Canonical theories of Langrangian dynamical systems in physics
Kastrup H.A. — Canonical theories of Langrangian dynamical systems in physics

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Canonical theories of Langrangian dynamical systems in physics

Автор: Kastrup H.A.


By reformulating the variational problem for a given classical Lagrangian field theory in the framework of differential forms, one can show
(Lepage) that for m a2 independent and for n>2 dependent (field) variables z" =f(x) a much wider variety of Legendre transformations
v% - ditf(x)-*Pa, L^>H, exists than has been employed in physics. The different canonical theories for a given Lagrangian can be classified
according to the rank of the corresponding basic canonical m-form. Each such canonical theory leads to a Hamilton-Jacobi theory, the "wave fronts" of which are transversal to solutions of the field equations.
Two canonical theories are discussed in more detail: The one by DeDonder and Weyl which employs the conventional canonical momenta pi = dL/dVp and the more sophisticated one by Caratheodory, the HJ theory of which is more intimately related to that of mechanics than the conventional one.
Generalizing results from mechanics one can show that each solution of a HJ equation which depends on a parameter generates a conserved current for those extremals which are transversal to that wave front.
The geometrically very rich, but algebraically rather complicated canonical formalism of Caratheodory provides interesting new approaches for the "qualitative" analysis of classical field theories. For instance: solutions of the field equations which give a vanishing Lagrangian density L are associated with singularities in the transversality relations between wave fronts and extremals.
A number of examples (strings, gauge theories etc.) illustrates the wealth of possible physical applications of these more general canonical formalisms for field theories, which, up to now, have been ignored almost completely by physicists.

Язык: en

Рубрика: Физика/Динамические системы/

Статус предметного указателя: Нет и не будет

ed2k: ed2k stats

Год издания: 1983

Количество страниц: 167

Добавлена в каталог: 13.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2021
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте