Generalized Duality, Hamiltonian Formalism and New Brackets

Автор(и)

  • S. Duplij Theory Group, Nuclear Physics Laboratory, V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv 61022, Ukraine

DOI:

https://doi.org/10.15407/mag10.02.189

Анотація

Показано, що будь-яка сингулярна лагранжева теорія: 1) може бути сформульована без залучення зв’язків за допомогою Клеро-версії гамільтонового формалізму; 2) приводить до спеціального вигляду неабелевої калібрувальної теорії, яка подібна до пуассонової калібрувальної теорії; 3) може бути сформульована як багаточасова класична динаміка. Узагальнення перетворення Лежандра на випадок нульового гессіана проведено з використанням змішаного (обгортаючого/загального) розв’язку багатовимірного рівняння Клеро. Рівняння руху записуються в гамільтоновій формі за допомогою введення нових антисиметричних дужок.  Відзначено, що будь-яка класична система з виродженим лагранжіаном еквівалентна багатовимірній класичній динаміці. На закінчення наведено взаємовідношення представленого формалізму й теорії зв’язків Дірака.

Mathematics Subject Classification: 37J05, 44A15, 49K20, 70H45.

Ключові слова:

зв’язки Дірака, неабелева калібрувальна теорія, вироджений лагранжіан, гессіан, перетворення Лежандра, багатовимірне рівняння Клеро, калібрувальна свобода, дужка Пуассона, багатовимірна динаміка

Посилання

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Duplij, S. Generalized Duality, Hamiltonian Formalism and New Brackets. Журн. мат. фіз. анал. геом. 2014, 10, 189-220.

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