{"id":416,"date":"2013-05-31T16:33:21","date_gmt":"2013-05-31T23:33:21","guid":{"rendered":"http:\/\/www.dereviankogroup.com\/?p=416"},"modified":"2014-11-21T06:37:51","modified_gmt":"2014-11-21T14:37:51","slug":"tutorial-on-translating-particle-physics-effective-lagrangians-to-conventional-atomic-physics-and-quantum-chemistry-operators","status":"publish","type":"post","link":"https:\/\/www.dereviankogroup.com\/dereviankogroup\/rightthere\/tutorial-on-translating-particle-physics-effective-lagrangians-to-conventional-atomic-physics-and-quantum-chemistry-operators\/","title":{"rendered":"Tutorial on translating particle physics effective Lagrangians to conventional atomic physics and quantum chemistry operators"},"content":{"rendered":"<p>Occasionally we have to carry out calculations with some effective Lagrangians<br \/>\nsupplied by our particle physics friends (possibly related to new physics<br \/>\nbeyond the standard model). For example, we could be given a Lagrangian density<br \/>\n<p style='text-align:center;'><span class='MathJax_Preview'><img data-recalc-dims=\"1\" src=\"https:\/\/i0.wp.com\/www.dereviankogroup.com\/dereviankogroup\/rightthere\/wp-content\/plugins\/latex\/cache\/tex_7d7a453ef4e752c5ed5e2ed7b3485367.gif?w=625&#038;ssl=1\" style='vertical-align: middle; border: none;' class='tex' alt=\"\" \/><\/span><script type='math\/tex;  mode=display'><\/script><\/p><br \/>\nwhere <span class='MathJax_Preview'><img data-recalc-dims=\"1\" src=\"https:\/\/i0.wp.com\/www.dereviankogroup.com\/dereviankogroup\/rightthere\/wp-content\/plugins\/latex\/cache\/tex_1ed346930917426bc46d41e22cc525ec.gif?w=625&#038;ssl=1\" style='vertical-align: middle; border: none; ' class='tex' alt=\"\" \/><\/span><script type='math\/tex'><\/script> is some scalar field, <span class='MathJax_Preview'><img data-recalc-dims=\"1\" src=\"https:\/\/i0.wp.com\/www.dereviankogroup.com\/dereviankogroup\/rightthere\/wp-content\/plugins\/latex\/cache\/tex_a11bd56a0ff5973a5604bb3fc9142b1d.gif?w=625&#038;ssl=1\" style='vertical-align: middle; border: none; ' class='tex' alt=\"\" \/><\/span><script type='math\/tex'><\/script> is the Dirac field (electrons) and <span class='MathJax_Preview'><img data-recalc-dims=\"1\" src=\"https:\/\/i0.wp.com\/www.dereviankogroup.com\/dereviankogroup\/rightthere\/wp-content\/plugins\/latex\/cache\/tex_b2f5ff47436671b6e533d8dc3614845d.gif?w=625&#038;ssl=1\" style='vertical-align: middle; border: none; padding-bottom:1px;' class='tex' alt=\"\" \/><\/span><script type='math\/tex'><\/script> is a coupling constant. The Dirac equation that is conventionally used in atomic physics reads <p style='text-align:center;'><span class='MathJax_Preview'><img data-recalc-dims=\"1\" src=\"https:\/\/i0.wp.com\/www.dereviankogroup.com\/dereviankogroup\/rightthere\/wp-content\/plugins\/latex\/cache\/tex_e82d12d1936faf4798cc5ea81e815cf4.gif?w=625&#038;ssl=1\" style='vertical-align: middle; border: none;' class='tex' alt=\"\" \/><\/span><script type='math\/tex;  mode=display'><\/script><\/p> (I suppress interactions of electrons with each other and with the nucleus). Given <span class='MathJax_Preview'><img data-recalc-dims=\"1\" src=\"https:\/\/i0.wp.com\/www.dereviankogroup.com\/dereviankogroup\/rightthere\/wp-content\/plugins\/latex\/cache\/tex_8e3310e75f7296cc221a8959b7470929.gif?w=625&#038;ssl=1\" style='vertical-align: middle; border: none; ' class='tex' alt=\"\" \/><\/span><script type='math\/tex'><\/script> what is that extra operator <span class='MathJax_Preview'><img data-recalc-dims=\"1\" src=\"https:\/\/i0.wp.com\/www.dereviankogroup.com\/dereviankogroup\/rightthere\/wp-content\/plugins\/latex\/cache\/tex_800e87ecca7d9069d11271599eb055b6.gif?w=625&#038;ssl=1\" style='vertical-align: middle; border: none; ' class='tex' alt=\"\" \/><\/span><script type='math\/tex'><\/script> that I would have to add to my Dirac Hamiltonian? I consistently derive <span class='MathJax_Preview'><img data-recalc-dims=\"1\" src=\"https:\/\/i0.wp.com\/www.dereviankogroup.com\/dereviankogroup\/rightthere\/wp-content\/plugins\/latex\/cache\/tex_800e87ecca7d9069d11271599eb055b6.gif?w=625&#038;ssl=1\" style='vertical-align: middle; border: none; ' class='tex' alt=\"\" \/><\/span><script type='math\/tex'><\/script> <a href=\"https:\/\/www.dereviankogroup.com\/dereviankogroup\/rightthere\/wp-content\/uploads\/2013\/05\/tutorial-dirac-public.pdf\">in this tutorial (pdf)<\/a>.<\/p>\n<p>For the impatient, the result is \\begin{equation}<br \/>\nV^{\\prime}\\psi=-\\gamma_{0}\\left( \\frac{\\partial\\mathcal{L}^{\\prime}}<br \/>\n{\\partial\\bar{\\psi}}-\\partial_{\\mu}\\left( \\frac{\\partial\\mathcal{L}^{\\prime}<br \/>\n}{\\partial\\left( \\partial_{\\mu}\\bar{\\psi}\\right) }\\right) \\right) .<br \/>\n\\end{equation} Applications to axions and \"Higgs portal\" interactions are also covered <a href=\"https:\/\/www.dereviankogroup.com\/dereviankogroup\/rightthere\/wp-content\/uploads\/2013\/05\/tutorial-dirac-public.pdf\">in the tutorial (pdf)<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Occasionally we have to carry out calculations with some effective Lagrangians supplied by our particle physics friends (possibly related to new physics beyond the standard model). For example, we could be given a Lagrangian density where is some scalar field, is the Dirac field (electrons) and is a coupling constant. The Dirac equation that is [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[21,12],"tags":[],"class_list":["post-416","post","type-post","status-publish","format-standard","hentry","category-dark-matter","category-physics"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Tutorial on translating particle physics effective Lagrangians to conventional atomic physics and quantum chemistry operators - Derevianko Group<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.dereviankogroup.com\/dereviankogroup\/rightthere\/tutorial-on-translating-particle-physics-effective-lagrangians-to-conventional-atomic-physics-and-quantum-chemistry-operators\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Tutorial on translating particle physics effective Lagrangians to conventional atomic physics and quantum chemistry operators - Derevianko Group\" \/>\n<meta property=\"og:description\" content=\"Occasionally we have to carry out calculations with some effective Lagrangians supplied by our particle physics friends (possibly related to new physics beyond the standard model). For example, we could be given a Lagrangian density where is some scalar field, is the Dirac field (electrons) and is a coupling constant. 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