{"id":353230,"date":"2017-01-16T03:00:00","date_gmt":"2017-01-16T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=e59fe5e64f24efad5cceb9d25dba12b9"},"modified":"2017-01-16T03:00:00","modified_gmt":"2017-01-16T00:00:00","slug":"combinatorics-in-tensor-integral-reduction","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=353230","title":{"rendered":"Combinatorics in tensor-integral reduction"},"content":{"rendered":"<p>We illustrate a rigorous approach to express the totally symmetric isotropic tensors of arbitrary<br \/>\nrank in the n -dimensional Euclidean space as a linear combination of products of Kronecker deltas.<br \/>\nBy making full use of the symmetries, one can greatly reduce the efforts to compute cumbersome<br \/>\nangular integrals into straightforward combinatoric counts. This method is generalised into the<br \/>\ncases in which such symmetries are present in subspaces. We further demonstrate the mechanism of the<br \/>\ntensor-integral reduction that is widely used in various physics problems such as perturbative<br \/>\ncalculations of the gauge-field theory in which divergent integrals are regularised in ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0143-0807\/38\/2\/025801\/ejpaa54ceieqn1.gif] {$d=4-2\\epsilon $} space\u2013time<br \/>\ndimensions. The main derivation is given in the n -dimensional Euclidean space. The generalisation<br \/>\nof the result to the Minkowski space is also discussed in order to provide graduat&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We illustrate a rigorous approach to express the totally symmetric isotropic tensors of arbitrary<br \/>\nrank in the n -dimensional Euclidean space as a linear combination of products of Kronecker deltas.<br \/>\nBy making full use of the symmetries, one can greatl&#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-353230","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\/353230","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=353230"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/353230\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=353230"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=353230"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=353230"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}