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Noether's Theorem and Symmetry

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ISBN: 9783039282340 9783039282357 Year: Pages: 186 DOI: 10.3390/books978-3-03928-235-7 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Law
Added to DOAB on : 2020-04-07 23:07:08
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Abstract

In Noether's 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 Noether's Theorem has been partly countered, in particular, in the review of Sarlet and Cantrijn. In this Special Issue, we emphasize the generality of Noether's 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.

Symmetry in Special and General Relativity

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ISBN: 9783039280940 9783039280957 Year: Pages: 100 DOI: 10.3390/books978-3-03928-095-7 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Physics (General) --- Science (General)
Added to DOAB on : 2020-01-30 16:39:46
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The development of special and general relativity has relied significantly on ideas of symmetry. Similarly, modern efforts to test these theories have often sought either violations or extensions of the symmetries seen, and symmetry is regularly used a tool in seeking new applications. In this Special Issue of symmetry, we explore some contemporary research related to symmetry in special and general relativity.

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2020 (2)