{"id":282046,"date":"2016-09-20T02:00:00","date_gmt":"2016-09-19T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=e473858d3fe845601d2c78db9d85c37c"},"modified":"2016-09-20T02:00:00","modified_gmt":"2016-09-19T23:00:00","slug":"pedagogical-systematic-derivation-of-noether-point-symmetries-in-special-relativistic-field-theoriesand-extended-gravity-cosmology","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=282046","title":{"rendered":"Pedagogical systematic derivation of Noether point symmetries in special relativistic field theories\r\nand extended gravity cosmology"},"content":{"rendered":"<p>A didactic and systematic derivation of Noether point symmetries and conserved currents is put<br \/>\nforward in special relativistic field theories, without a priori assumptions about the<br \/>\ntransformation laws. Given the Lagrangian density, the invariance condition develops as a set of<br \/>\npartial differential equations determining the symmetry transformation. The solution is provided in<br \/>\nthe case of real scalar, complex scalar, free electromagnetic, and charged electromagnetic fields.<br \/>\nBesides the usual conservation laws, a less popular symmetry is analyzed: the symmetry associated<br \/>\nwith the linear superposition of solutions, whenever applicable. The role of gauge invariance is<br \/>\nemphasized. The case of the charged scalar particle under external electromagnetic fields is<br \/>\nconsidered, and the accompanying Noether point symmetries determined. Noether point symmetries for a<br \/>\ndynamical system in extended gravity cosmology are also deduced.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A didactic and systematic derivation of Noether point symmetries and conserved currents is put<br \/>\nforward in special relativistic field theories, without a priori assumptions about the<br \/>\ntransformation laws. Given the Lagrangian density, the invariance co&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-282046","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/282046","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=282046"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/282046\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=282046"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=282046"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=282046"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}