{"id":95877,"date":"2015-06-18T03:00:00","date_gmt":"2015-06-18T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=2f71c0c22cc132211224fd4931d2b2ed"},"modified":"2015-06-18T03:00:00","modified_gmt":"2015-06-18T00:00:00","slug":"gauge-invariance-in-simple-mechanical-systems","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=95877","title":{"rendered":"Gauge invariance in simple mechanical systems"},"content":{"rendered":"<p>This article discusses and explains the Hamiltonian formulation for a class of simple gauge<br \/>\ninvariant mechanical systems consisting of point masses and idealized rods. The study of these<br \/>\nmodels may be helpful to advanced undergraduate or graduate students in theoretical physics to<br \/>\nunderstand, in a familiar context, some concepts relevant to the study of classical and quantum<br \/>\nfield theories. We use a geometric approach to derive the Hamiltonian formulation for the model<br \/>\nconsidered in the paper: four equal masses connected by six ideal rods. We obtain and discuss the<br \/>\nmeaning of several important elements, in particular, the constraints and the Hamiltonian vector<br \/>\nfields that define the dynamics of the system, the constraint manifold, gauge symmetries, gauge<br \/>\norbits, gauge fixing, and the reduced phase space.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This article discusses and explains the Hamiltonian formulation for a class of simple gauge<br \/>\ninvariant mechanical systems consisting of point masses and idealized rods. The study of these<br \/>\nmodels may be helpful to advanced undergraduate or graduate stu&#8230;<\/p>\n","protected":false},"author":0,"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-95877","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\/95877","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"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=95877"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/95877\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=95877"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=95877"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=95877"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}