{"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":"2020-02-18T14:28:38","modified_gmt":"2020-02-18T13:28:38","slug":"matematicka-fizika","status":"publish","type":"post","link":"https:\/\/www.pmfst.unist.hr\/znanost\/matematicka-fizika\/","title":{"rendered":"Matemati\u010dka fizika"},"content":{"rendered":"
[vc_row][vc_column width=”1\/4″][mk_title_box color=”#1e73be” font_family=”none”]Odjel\/Katedra: <\/strong>
\nOdjel za fiziku[\/mk_title_box][mk_employees column=”1″ custom_image_size=”true” image_size=”medium” rounded_image=”false” grayscale_image=”false” employees=”18768″][\/vc_column][vc_column width=”3\/4″][vc_column_text css=”.vc_custom_1520254767360{margin-bottom: 0px !important;}”]\n

Podru\u010dje istra\u017eivanja:<\/h4>\n

– Nekomutativna geometrija
\n– Liejeve algebre i superalgebre
\n– Integrabilni sistemi
\n– Simetrije[\/vc_column_text][vc_column_text css=”.vc_custom_1520254804248{margin-bottom: 0px !important;}”]\n

Opis istra\u017eivanja:<\/h4>\n

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=”.vc_custom_1520255081520{margin-bottom: 0px !important;}”]\n

Kontakti s akademskim i drugim institucijama:<\/strong><\/h4>\n

– Institut Ru\u0111er Bo\u0161kovi\u0107
\n– Institute of Theoretical Physics, University of Wroclaw
\n– Department of Mathematics, University of Georgia, USA
\n– KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Sciences[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text css=”.vc_custom_1520255111442{margin-bottom: 0px !important;}”]\n

Opis dosada\u0161nje suradnje:<\/strong><\/h4>\n

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=”.vc_custom_1520255130633{margin-bottom: 0px !important;}”]\n

Planovi budu\u0107ih istra\u017eivanja:<\/strong><\/h4>\n

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=”.vc_custom_1520255161585{margin-bottom: 0px !important;}”]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.
\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.
\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.
\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.
\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.
\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.
\n7. S. Kre\u0161i\u0107-Juri\u0107, The Heisenberg magnet equation and the Birkhoff factorization, Ann. Univ. Ferrara 53 (2007), 299-308.
\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.
\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_row]\n<\/div>","protected":false},"excerpt":{"rendered":"

[vc_row][vc_column width=”1\/4″][mk_title_box color=”#1e73be” font_family=”none”]Odjel\/Katedra: Odjel za fiziku[\/mk_title_box][mk_employees column=”1″ custom_image_size=”true” image_size=”medium” rounded_image=”false” grayscale_image=”false” employees=”18768″][\/vc_column][vc_column width=”3\/4″][vc_column_text css=”.vc_custom_1520254767360{margin-bottom: 0px !important;}”] Podru\u010dje istra\u017eivanja: – Nekomutativna geometrija – Liejeve algebre i superalgebre – Integrabilni sistemi – Simetrije[\/vc_column_text][vc_column_text css=”.vc_custom_1520254804248{margin-bottom: 0px !important;}”] Opis istra\u017eivanja: Istra\u017euju se matemati\u010dke teorije koje imaju primjenu u formulaciji kvantne gravitacije i opisu strukture prostor-vremena na Planckovoj skali. […]<\/p>\n","protected":false},"author":1,"featured_media":885,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"diplosmki-rad":"","smjer_obrana_radova":"","footnotes":""},"categories":[11,26],"tags":[],"poredak":[],"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":"\nMatemati\u010dka fizika - Znanstvena djelatnost, PMF Split<\/title>\n<meta name=\"robots\" content=\"noindex, follow\" \/>\n<meta property=\"og:locale\" content=\"hr_HR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Matemati\u010dka fizika - Znanstvena djelatnost, PMF Split\" \/>\n<meta property=\"og:description\" content=\"[vc_row][vc_column width=”1\/4″][mk_title_box color=”#1e73be” font_family=”none”]Odjel\/Katedra: Odjel za fiziku[\/mk_title_box][mk_employees column=”1″ custom_image_size=”true” image_size=”medium” rounded_image=”false” grayscale_image=”false” employees=”18768″][\/vc_column][vc_column width=”3\/4″][vc_column_text css=”.vc_custom_1520254767360{margin-bottom: 0px !important;}”] Podru\u010dje istra\u017eivanja: – Nekomutativna geometrija – Liejeve algebre i superalgebre – Integrabilni sistemi – Simetrije[\/vc_column_text][vc_column_text css=”.vc_custom_1520254804248{margin-bottom: 0px !important;}”] Opis istra\u017eivanja: Istra\u017euju se matemati\u010dke teorije koje imaju primjenu u formulaciji kvantne gravitacije i opisu strukture prostor-vremena na Planckovoj skali. 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Znanstvena djelatnost, PMF Split","robots":{"index":"noindex","follow":"follow"},"og_locale":"hr_HR","og_type":"article","og_title":"Matemati\u010dka fizika - Znanstvena djelatnost, PMF Split","og_description":"[vc_row][vc_column width=”1\/4″][mk_title_box color=”#1e73be” font_family=”none”]Odjel\/Katedra: Odjel za fiziku[\/mk_title_box][mk_employees column=”1″ custom_image_size=”true” image_size=”medium” rounded_image=”false” grayscale_image=”false” employees=”18768″][\/vc_column][vc_column width=”3\/4″][vc_column_text css=”.vc_custom_1520254767360{margin-bottom: 0px !important;}”] Podru\u010dje istra\u017eivanja: – Nekomutativna geometrija – Liejeve algebre i superalgebre – Integrabilni sistemi – Simetrije[\/vc_column_text][vc_column_text css=”.vc_custom_1520254804248{margin-bottom: 0px !important;}”] Opis istra\u017eivanja: Istra\u017euju se matemati\u010dke teorije koje imaju primjenu u formulaciji kvantne gravitacije i opisu strukture prostor-vremena na Planckovoj skali. 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