Details

Autor(en) / Beteiligte

• Leach, P.G.L
• Paliathanasis, Andronikos

Titel

Noethers Theorem and Symmetry

Ort / Verlag

MDPI - Multidisciplinary Digital Publishing Institute

Erscheinungsjahr

2020

Beschreibungen/Notizen

• Open Access
• In Noethers original presentation of her celebrated theorem of 1918, allowances were made for the dependence of the coefficient functions of the differential operator which generated the infinitesimal transformation of the Action Integral upon the derivatives of the dependent variable(s), the so-called generalized, or dynamical, symmetries. A similar allowance is to be found in the variables of the boundary function, often termed a gauge function by those who have not read the original paper. This generality was lost after texts such as those of Courant and Hilbert or Lovelock and Rund confined attention to only point transformations. In recent decades, this diminution of the power of Noethers Theorem has been partly countered, in particular, in the review of Sarlet and Cantrijn. In this Special Issue, we emphasize the generality of Noethers Theorem in its original form and explore the applicability of even more general coefficient functions by allowing for nonlocal terms. We also look at the application of these more general symmetries to problems in which parameters or parametric functions have a more general dependence upon the independent variables
• English