Open AccessEmmy Noether and Linear Evolution Equations
Author(s) -
P. G. L. Leach
Publication year - 2013
Publication title -
acta polytechnica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.207
H-Index - 15
eISSN - 1805-2363
pISSN - 1210-2709
DOI - 10.14311/1811
Subject(s) - noether's theorem , homogeneous space , lagrangian , mathematics , invariant (physics) , mathematical physics , action (physics) , variational principle , luke's variational principle , gauge symmetry , conservation law , extension (predicate logic) , hamilton's principle , mathematical analysis , classical mechanics , physics , equations of motion , geometry , quantum mechanics , gauge theory , computer science , programming language
Noether’s Theorem relates the Action Integral of a Lagrangian with symmetries which leave it invariant and the first integrals consequent upon the variational principle and the existence of the symmetries. These each have an equivalent in the Schrödinger Equation corresponding to the Lagrangian and by extension to linear evolution equations in general. The implications of these connections are investigated.