Jump to ContentJump to Main Navigation
Lagrangian and Hamiltonian Dynamics$
Users without a subscription are not able to see the full content.

Peter Mann

Print publication date: 2018

Print ISBN-13: 9780198822370

Published to Oxford Scholarship Online: August 2018

DOI: 10.1093/oso/9780198822370.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 24 June 2021

Lagrangian Field Theory

Lagrangian Field Theory

Chapter:
(p.345) 25 Lagrangian Field Theory
Source:
Lagrangian and Hamiltonian Dynamics
Author(s):

Peter Mann

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198822370.003.0025

In this chapter, Hamiltonian field theory is derived classically via a Hamiltonian density, using the zeroth component of a 4-momentum density. In field theory, space and time are considered to be on equal footing but, in the canonical formalism, time is treated as being special and therefore, by definition, it is not covariant. Consequently, most field theoretic models are built on Lagrangian formulations. A covariant canonical formalism is the subject of the de Donder–Weyl formalism, which is briefly discussed as a covariant Hamiltonian field theory. In addition, the chapter examines the case of a generalised Poisson bracket in the continuous form for two local smooth functionals of phase space.

Keywords:   Hamiltonian density, 4-momentum density, de Donder–Weyl, Hamiltonian field theory, Poisson bracket

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .