{"id":884,"date":"2018-03-05T13:59:30","date_gmt":"2018-03-05T12:59:30","guid":{"rendered":"https:\/\/www.pmfst.unist.hr\/znanost\/?p=884"},"modified":"2018-05-17T14:11:35","modified_gmt":"2018-05-17T12:11:35","slug":"matematicka-fizika","status":"publish","type":"post","link":"https:\/\/www.pmfst.unist.hr\/odjel-za-matematiku\/matematicka-fizika\/","title":{"rendered":"Matemati\u010dka fizika"},"content":{"rendered":"<div class=\"wpb-content-wrapper\">[vc_row][vc_column width=&#8221;3\/6&#8243;][mk_icon_box icon=&#8221;mk-moon-man&#8221; title=&#8221;prof.dr.sc. Sa\u0161a Kre\u0161i\u0107-Juri\u0107&#8221; text_size=&#8221;20&#8243; style=&#8221;boxed&#8221; icon_color=&#8221;#1e73be&#8221; icon_circle_color=&#8221;&#8221; icon_circle_border_color=&#8221;#1e73be&#8221; title_color=&#8221;#1e73be&#8221;]<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.pmfst.unist.hr\/wp-content\/uploads\/2015\/02\/sasakresicjuric.jpg\" alt=\"\" width=\"180\" height=\"180\" \/><\/p>\n<p>&nbsp;<\/p>\n<ul>\n<li>tel: +385 21 619 2228<\/li>\n<li><strong><a style=\"color: #3366ff;\" href=\"https:\/\/www.pmfst.unist.hr\/wp-content\/uploads\/2017\/12\/ana_8940.jpg\">kabinet B2-32<\/a><\/strong><\/li>\n<li><a href=\"mailto:skresic@pmfst.hr\">skresic@pmfst.hr<\/a><\/li>\n<\/ul>\n[\/mk_icon_box][\/vc_column][vc_column width=&#8221;2\/6&#8243;][mk_title_box color=&#8221;#1e73be&#8221; font_family=&#8221;none&#8221;]<strong>Odjel\/Katedra: <\/strong><\/p>\n<p>Odjel za matematiku[\/mk_title_box][vc_column_text css=&#8221;.vc_custom_1520254767360{margin-bottom: 0px !important;}&#8221;]\n<h4>Podru\u010dje istra\u017eivanja:<\/h4>\n<p>&#8211; Nekomutativna geometrija<br \/>\n&#8211; Liejeve algebre i superalgebre<br \/>\n&#8211; Integrabilni sistemi<br \/>\n&#8211; Simetrije[\/vc_column_text][\/vc_column][vc_column width=&#8221;1\/6&#8243;][\/vc_column][\/vc_row][vc_row][vc_column width=&#8221;5\/6&#8243;][vc_separator color=&#8221;mulled_wine&#8221; style=&#8221;shadow&#8221; border_width=&#8221;3&#8243;][\/vc_column][vc_column width=&#8221;1\/6&#8243;][\/vc_column][\/vc_row][vc_row][vc_column width=&#8221;5\/6&#8243;][vc_column_text css=&#8221;.vc_custom_1520254804248{margin-bottom: 0px !important;}&#8221;]\n<h4>Opis istra\u017eivanja:<\/h4>\n<p>Istra\u017euju se matemati\u010dke teorije koje imaju primjenu u formulaciji kvantne gravitacije i opisu strukture prostor-vremena na Planckovoj skali. Naglasak je dan na istra\u017eivanju nekomutativnih prostora tipa Liejeve algebre i algebarskom pristupu u formulaciji diferencijalne geometrije na takvim prostorima. Standardni pojmovi iz diferencijalne geometrije se konstruiraju kao deformacije odgovaraju\u0107ih klasi\u010dnih pojmova gdje su parametri deformacije strukturne konstante Liejeve superalgebre. Istra\u017eivanje uklju\u010duju: (1) svojstva omota\u010dkih algebri kona\u010dnodimenzionalnih Liejevih algebri i Liejevih superalgebri, te njihova ulaganje u Weylove u Clifford-Weylove algebre, (2) deformirane simetrije nekomutativnih prostora, (3) veze izme\u0111u omota\u010dkih algebri, Hopfove strukture i zvijezda-umno\u0161ka na simetri\u010dnim algebrama, (4) konstrukcija bikovarijantnih diferencijalnih ra\u010duna na kvantnim prostorima i njihove realizacije u Clifford-Weylovoj algebri, (5) algebarske metode za integrabilne sisteme i njihove diskretizacije. Budu\u0107a istra\u017eivanja uklju\u010duju formulaciju diferencijalnih ra\u010duna vi\u0161eg reda, Liejevu derivaciju, Hodgeov operator i druge geometrijske objekte u okviru teorije deformacije. Tako\u0111er \u0107e se istra\u017eivati geometrijske metode za numeri\u010dku integraciju integrabilnih sistema u klasi\u010dnoj i kvantnoj mehanici.[\/vc_column_text][vc_column_text css=&#8221;.vc_custom_1520255081520{margin-bottom: 0px !important;}&#8221;]\n<h4><strong>Kontakti s akademskim i drugim institucijama:<\/strong><\/h4>\n<p>&#8211; Institut Ru\u0111er Bo\u0161kovi\u0107<br \/>\n&#8211; Institute of Theoretical Physics, University of Wroclaw<br \/>\n&#8211; Department of Mathematics, University of Georgia, USA<br \/>\n&#8211; KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Sciences[\/vc_column_text][\/vc_column][vc_column width=&#8221;1\/6&#8243;][\/vc_column][\/vc_row][vc_row][vc_column width=&#8221;5\/6&#8243;][vc_column_text css=&#8221;.vc_custom_1520255111442{margin-bottom: 0px !important;}&#8221;]\n<h4><strong>Opis dosada\u0161nje suradnje:<\/strong><\/h4>\n<p>Istra\u017eivanja na nekomutativnim prostorima provedena su u suradnji s Grupom za matemati\u010dku fiziku pri Institutu Ru\u0111er Bo\u0161kovi\u0107. Istra\u017eivanja u podru\u010dju integrabilnih sistema su provedena u suradnji s Department of Mathematics, Unversity of Georgia, USA.[\/vc_column_text][vc_column_text css=&#8221;.vc_custom_1520255130633{margin-bottom: 0px !important;}&#8221;]\n<h4><strong>Planovi budu\u0107ih istra\u017eivanja:<\/strong><\/h4>\n<p>U budu\u0107nosti planiramo nastaviti istra\u017eivanja u podru\u010dju diferencijalne geometrije na kvantnim prostorima i realizacijama Liejevih superalgebri. Ovo ukju\u010duje istra\u017eivanje drugih tipova diferencijalnog ra\u010duna na nekomutativnim prostorima tipa Lijeve algebre kao i upotrebu teorije deformacije u prou\u010davanju drugih tipova kvantnih prostora. Tako\u0111er \u0107emo mo\u017eda istra\u017eivati metode Liejevih grupa za numeri\u010dku integraciju evolucijskih jednad\u017ebi.[\/vc_column_text][vc_column_text css=&#8221;.vc_custom_1520255161585{margin-bottom: 0px !important;}&#8221;]1. S. Meljanac, S. Kre\u0161i\u0107-Juri\u0107, T. Martini\u0107, The Weyl realizations of Lie algebras, and left-right duaity, J. Math. Phys. 57 (2016), 051704.<br \/>\n2. S. Meljanac, S. Kre\u0161i\u0107-Juri\u0107, R. \u0160trajn, Differential algebras on kappa-Minkowski space and action of the Lorentz algebra, Int. J. Mod. Phys. A 27 (10) (2012), 1250057.<br \/>\n3. S. Meljanac, S. Kre\u0161i\u0107-Juri\u0107, Differential structure on kappa-Minkowski space, andkappa-Poincare algebra, Int. J. Mod. Phys. A 26 (20) (2011), 3385-3402.<br \/>\n4. S. Meljanac, S. Kre\u0161i\u0107-Juri\u0107, Noncommutative differential forms on the kappa-deformed space, J. Phys. A: Math. Theor. 42 (2009), 3652014.<br \/>\n5. S. Meljanac, S. Kre\u0161i\u0107-Juri\u0107, Generalized kappa-deformed spaces, star-products, and their realizations, J. Phys. A: Math. Theor. 41 (2008), 235203.<br \/>\n6. T. Fukuyama, K. Kamimura, S. Kre\u0161i\u0107-Juri\u0107, S. Meljanac, Gauge transformations and symmetries of integrable systems, J. Phys. A: Math. Theor. 40 (2007), 12227-12241.<br \/>\n7. S. Kre\u0161i\u0107-Juri\u0107, The Heisenberg magnet equation and the Birkhoff factorization, Ann. Univ. Ferrara 53 (2007), 299-308.<br \/>\n8. S. Meljanac, S. Kre\u0161i\u0107-Juri\u0107, M. Stoji\u0107, Covariant realizations of kappa-deformed space, Eur. Phys. J. C 51 (2007) 229-240.<br \/>\n9. S. Kre\u0161i\u0107-Juri\u0107, On the Birkhoff factorization problem for the Heisenberg magnet and nonlinear Schroedinger equations, J. Math. Phys. 47 (2006), 063501.[\/vc_column_text][\/vc_column][vc_column width=&#8221;1\/6&#8243;][\/vc_column][\/vc_row]\n<\/div>","protected":false},"excerpt":{"rendered":"<p>[vc_row][vc_column width=&#8221;3\/6&#8243;][mk_icon_box icon=&#8221;mk-moon-man&#8221; title=&#8221;prof.dr.sc. Sa\u0161a Kre\u0161i\u0107-Juri\u0107&#8221; text_size=&#8221;20&#8243; style=&#8221;boxed&#8221; icon_color=&#8221;#1e73be&#8221; icon_circle_color=&#8221;&#8221; icon_circle_border_color=&#8221;#1e73be&#8221; title_color=&#8221;#1e73be&#8221;] &nbsp; tel: +385 21 619 2228 kabinet B2-32 skresic@pmfst.hr [\/mk_icon_box][\/vc_column][vc_column width=&#8221;2\/6&#8243;][mk_title_box color=&#8221;#1e73be&#8221; font_family=&#8221;none&#8221;]Odjel\/Katedra: Odjel za matematiku[\/mk_title_box][vc_column_text css=&#8221;.vc_custom_1520254767360{margin-bottom: 0px !important;}&#8221;] Podru\u010dje istra\u017eivanja: &#8211; Nekomutativna geometrija &#8211; Liejeve algebre i superalgebre &#8211; Integrabilni sistemi &#8211; Simetrije[\/vc_column_text][\/vc_column][vc_column width=&#8221;1\/6&#8243;][\/vc_column][\/vc_row][vc_row][vc_column width=&#8221;5\/6&#8243;][vc_separator color=&#8221;mulled_wine&#8221; style=&#8221;shadow&#8221; border_width=&#8221;3&#8243;][\/vc_column][vc_column width=&#8221;1\/6&#8243;][\/vc_column][\/vc_row][vc_row][vc_column width=&#8221;5\/6&#8243;][vc_column_text css=&#8221;.vc_custom_1520254804248{margin-bottom: 0px [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1461,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"rs_blank_template":"","rs_page_bg_color":"","slide_template_v7":"","footnotes":""},"categories":[9,4],"tags":[],"class_list":["post-884","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-odjel-za-matematiku","category-samostalna-istrazivanja"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Matemati\u010dka fizika - Odjel za matematiku<\/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.pmfst.unist.hr\/odjel-za-matematiku\/matematicka-fizika\/\" \/>\n<meta property=\"og:locale\" content=\"hr_HR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Matemati\u010dka fizika - Odjel za matematiku\" \/>\n<meta property=\"og:description\" content=\"[vc_row][vc_column width=&#8221;3\/6&#8243;][mk_icon_box icon=&#8221;mk-moon-man&#8221; title=&#8221;prof.dr.sc. 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