Abstract
A generalized first Noether theorem (GFNT) originating from the invariance under the finite continuous group for singular high-order Lagrangian and a generalized second Noether theorem (or generalized Noether identities (GNI)) for variant system under the infinite continuous group of field theory in canonical formalism are derived. The strong and weak conservation laws in canonical formalism are also obtained. It is pointed out that some variant systems also have Dirac constraint. Based on the canonical action, the generalized Poincare-Cartan integral invariant (GPCⅡ) for singular high-order Lagrangian in the field theory is deduced. Some confusions in literafure are clarified. The GPCⅡ connected with canonical equations and canonical transformation are discussed.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Science in China Series A-Mathematics, Physics, Astronomy & Technological Science
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
