Physics – Mathematical Physics
Scientific paper
2001-11-21
Rept.Math.Phys. 53 (2004) 19-37
Physics
Mathematical Physics
23 pages
Scientific paper
This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to $L_VY$, the bundle of vertically adapted linear frames over the bundle of field configurations $Y$. Specifically, the generalized field momentum observables are vector-valued momentum mappings on the vertically adapted frame bundle generated from automorphisms of $Y$. The generalized symplectic geometry on $L_VY$ is a covering theory for multisymplectic geometry on the multiphase space $Z$, and it follows that the field momentum observables on $Z$ are generalized by those on $L_VY$. Furthermore, momentum observables on $L_VY$ produce conserved quantities along flows in $L_VY$. For translational and orthogonal symmetries of fields and reparametrization symmetry in mechanics, momentum is conserved, and for angular momentum in time-evolution mechanics we produce a version of the parallel axis theorem of rotational dynamics, and in special relativity, we produce the transformation of angular momentum under boosts.
No associations
LandOfFree
A Frame Bundle Generalization of Multisymplectic Momentum Mappings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Frame Bundle Generalization of Multisymplectic Momentum Mappings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Frame Bundle Generalization of Multisymplectic Momentum Mappings will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-341767