Editing Mathematical physics (section)

=== Classical mechanics ===
{{Main|Lagrangian mechanics|Hamiltonian mechanics}}
Applying the techniques of mathematical physics to classical mechanics typically involves the rigorous, abstract, and advanced reformulation of Newtonian mechanics in terms of [[Lagrangian mechanics]] and [[Hamiltonian mechanics]] (including both approaches in the presence of constraints). Both formulations are embodied in [[analytical mechanics]] and lead to an understanding of the deep interplay between the notions of [[symmetry (physics)|symmetry]] and [[conservation law|conserved quantities]] during the dynamical evolution of mechanical systems, as embodied within the most elementary formulation of [[Noether's theorem]]. These approaches and ideas have been extended to other areas of physics, such as [[statistical mechanics]], [[continuum mechanics]], [[classical field theory]], and [[quantum field theory]]. Moreover, they have provided multiple examples and ideas in [[differential geometry]] (e.g., several notions in [[symplectic geometry]] and [[vector bundle]]s).