. . . . . . . . . . . . . . . . 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"\uBB3C\uB9AC\uD559\uACFC \uC218\uD559\uC5D0\uC11C \uC704\uC0C1 \uC591\uC790\uC7A5\uB860(\u4F4D\u76F8\u91CF\u5B50\u5834\u8AD6, \uC601\uC5B4: topological quantum field theory, \uC57D\uC790 TQFT)\uC740 \uACC4\uB7C9 \uD150\uC11C\uC5D0 \uC758\uC874\uD558\uC9C0 \uC54A\uB294 \uC591\uC790\uC7A5\uB860\uC774\uB2E4. \uBBF8\uBD84\uAD6C\uC870\uC870\uCC28 \uACE0\uB824\uD558\uC9C0 \uC54A\uB294 \uC704\uC0C1\uB2E4\uC591\uCCB4\uC5D0\uC11C \uD558\uB294 \uAC83\uC740 \uC544\uB2C8\uACE0, \uC815\uD655\uD788\uB294 \uB9AC\uB9CC \uACC4\uB7C9\uC744 \uACE0\uB824\uD558\uC9C0 \uC54A\uB294 \uBBF8\uBD84\uB2E4\uC591\uCCB4\uC704\uC5D0\uC11C \uD558\uBBC0\uB85C \uC704\uC0C1 \uC591\uC790\uC7A5\uB860\uBCF4\uB2E4\uB294 \uBBF8\uBD84 \uC704\uC0C1 \uC591\uC790\uC7A5\uB860\uC774 \uB354 \uC5B4\uC6B8\uB9AC\uB294 \uC774\uB984\uC774\uB2E4. \uC785\uC790 \uBB3C\uB9AC\uD559\uACFC \uB048 \uC774\uB860, \uC751\uC9D1\uBB3C\uC9C8\uBB3C\uB9AC\uD559\uACFC \uB300\uC218\uC801 \uC704\uC0C1\uC218\uD559, \uB9E4\uB4ED \uC774\uB860\uC5D0\uC11C \uC4F0\uC778\uB2E4."@ko . . "27076"^^ . . . . "\u62D3\u64B2\u91CF\u5B50\u5834\u8AD6"@zh . . . . . . "\u4F4D\u76F8\u7684\u5834\u306E\u7406\u8AD6\uFF08\u3044\u305D\u3046\u3066\u304D\u3070\u306E\u308A\u308D\u3093\uFF09\u3082\u3057\u304F\u306F\u4F4D\u76F8\u5834\u7406\u8AD6\uFF08\u3044\u305D\u3046\u3070\u308A\u308D\u3093\uFF09\u3042\u308B\u3044\u306FTQFT\u306F\u3001\u4F4D\u76F8\u4E0D\u5909\u91CF\u3092\u8A08\u7B97\u3059\u308B\u5834\u306E\u91CF\u5B50\u8AD6\u3067\u3042\u308B\u3002 TQFT\u306F\u7269\u7406\u5B66\u8005\u306B\u3088\u308A\u958B\u62D3\u3055\u308C\u305F\u306B\u3082\u304B\u304B\u308F\u3089\u305A\u3001\u6570\u5B66\u7684\u306B\u3082\u8208\u5473\u3092\u6301\u305F\u308C\u3066\u3044\u3066\u3001\u7D50\u3073\u76EE\u7406\u8AD6\u3084\u4EE3\u6570\u30C8\u30DD\u30ED\u30B8\u30FC\u306E 4\u6B21\u5143\u591A\u69D8\u4F53\u306E\u7406\u8AD6\u3084\u4EE3\u6570\u5E7E\u4F55\u5B66\u306E\u30E2\u30B8\u30E5\u30E9\u30A4\u7A7A\u9593\u306E\u7406\u8AD6\u3068\u3044\u3046\u4ED6\u306E\u3082\u306E\u306B\u3082\u95A2\u4FC2\u3057\u3066\u3044\u308B\u3002\u30B5\u30A4\u30E2\u30F3\u30FB\u30C9\u30CA\u30EB\u30C9\u30BD\u30F3, \u30F4\u30A9\u30FC\u30F3\u30FB\u30B8\u30E7\u30FC\u30F3\u30BA, \u30A8\u30C9\u30EF\u30FC\u30C9\u30FB\u30A6\u30A3\u30C3\u30C6\u30F3, \u3084 \u30DE\u30AD\u30B7\u30E0\u30FB\u30B3\u30F3\u30C4\u30A7\u30D3\u30C3\u30C1 \u306F\u7686\u3001\u30D5\u30A3\u30FC\u30EB\u30BA\u8CDE \u3092\u3068\u308A\u3001\u4F4D\u76F8\u7684\u5834\u306E\u7406\u8AD6\u306B\u95A2\u9023\u3057\u305F\u4ED5\u4E8B\u3092\u884C\u3063\u3066\u3044\u308B\u3002 \u7269\u6027\u7269\u7406\u5B66\u3067\u306F\u3001\u4F4D\u76F8\u7684\u5834\u306E\u7406\u8AD6\u306F\u3001\u5206\u6570\u91CF\u5B50\u30DB\u30FC\u30EB\u52B9\u679C\u3084\u3001\u51DD\u7E2E\u72B6\u614B\u3084\u4ED6\u306E\u72B6\u614B\u306E\u3088\u3046\u306A\u3001\u306E\u4F4E\u30A8\u30CD\u30EB\u30AE\u30FC\u6709\u52B9\u7406\u8AD6\u3067\u3042\u308B\u3002"@ja . . "\u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0645\u062C\u0627\u0644 \u0627\u0644\u0643\u0645\u064A \u0627\u0644\u0637\u0648\u0628\u0648\u0644\u0648\u062C\u064A\u0629 \u0623\u0648 \u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u062D\u0642\u0644 \u0627\u0644\u0637\u0648\u0628\u0648\u0644\u0648\u062C\u064A\u0629\u060C \u062A\u062D\u0633\u0628 \u0627\u0644\u062B\u0648\u0627\u0628\u062A \u0627\u0644\u0637\u0648\u0628\u0648\u0644\u0648\u062C\u064A\u0629. \u0628\u0627\u0644\u0631\u063A\u0645 \u0645\u0646 \u0623\u0646 \u0627\u0644\u0641\u064A\u0632\u064A\u0627\u0626\u064A\u064A\u0646 \u0647\u0645 \u0645\u0646 \u0627\u062E\u062A\u0631\u0639\u0648\u0627 \u0646\u0638\u0631\u064A\u0627\u062A \u0627\u0644\u0645\u062C\u0627\u0644 \u0627\u0644\u0643\u0645\u064A \u0627\u0644\u0637\u0648\u0628\u0648\u0644\u0648\u062C\u064A\u0629\u060C \u0647\u064A \u0623\u064A\u0636\u064B\u0627 \u0630\u0627\u062A \u0623\u0647\u0645\u064A\u0629 \u0631\u064A\u0627\u0636\u064A\u0629 \u0644\u0643\u0648\u0646\u0647\u0627 \u0645\u062A\u0639\u0644\u0642\u0629 \u0628\u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0639\u0642\u062F\u0629 \u0648\u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0645\u062A\u0634\u0639\u0628\u0627\u062A \u0627\u0644\u0623\u0631\u0628\u0639\u0629 \u0641\u064A \u0627\u0644\u0637\u0648\u0628\u0648\u0644\u0648\u062C\u064A\u0627 \u0627\u0644\u062C\u0628\u0631\u064A\u0629\u060C \u0648\u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0645\u0633\u0627\u062D\u0627\u062A \u0627\u0644\u0645\u0639\u064A\u0627\u0631\u064A\u0629 \u0641\u064A \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062C\u0628\u0631\u064A\u0629 \u0648\u063A\u064A\u0631\u0647\u0627 \u0645\u0646 \u0627\u0644\u0646\u0638\u0631\u064A\u0627\u062A. \u0641\u0627\u0632 \u0643\u0644 \u0645\u0646 \u062F\u0648\u0646\u0627\u0644\u062F\u0633\u0648\u0646 \u0648\u062C\u0648\u0646\u0632 \u0648\u0648\u064A\u062A\u0646 \u0648\u0643\u0648\u0646\u062A\u0633\u064A\u0641\u064A\u062A\u0634 \u0628\u0645\u064A\u062F\u0627\u0644\u064A\u0627\u062A \u0641\u064A\u0644\u062F\u0632 \u0644\u0644\u0639\u0645\u0644 \u0627\u0644\u0631\u064A\u0627\u0636\u064A \u0627\u0644\u0645\u062A\u0639\u0644\u0642 \u0628\u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0645\u062C\u0627\u0644 \u0627\u0644\u0637\u0648\u0628\u0648\u0644\u0648\u062C\u064A. \u0641\u064A \u0641\u064A\u0632\u064A\u0627\u0621 \u0627\u0644\u0645\u0648\u0627\u062F \u0627\u0644\u0645\u0643\u062B\u0641\u0629\u060C \u062A\u0639\u062A\u0628\u0631 \u0646\u0638\u0631\u064A\u0627\u062A \u0627\u0644\u0645\u062C\u0627\u0644 \u0627\u0644\u0643\u0645\u064A \u0627\u0644\u0637\u0648\u0628\u0648\u0644\u0648\u062C\u064A \u0646\u0638\u0631\u064A\u0627\u062A \u0641\u0639\u0627\u0644\u0629 \u0645\u0646\u062E\u0641\u0636\u0629 \u0627\u0644\u0637\u0627\u0642\u0629 \u0644\u0644\u062D\u0627\u0644\u0627\u062A \u0627\u0644\u0645\u0631\u062A\u0628\u0629 \u0637\u0648\u0628\u0648\u0644\u0648\u062C\u064A\u064B\u0627\u060C \u0645\u062B\u0644 \u0627\u0644\u062D\u0627\u0644\u0627\u062A \u0627\u0644\u0643\u0645\u064A\u0629 \u0627\u0644\u0643\u0633\u0631\u064A\u0629 \u0644\u0647\u0648\u0644\u060C \u0648\u0627\u0644\u062D\u0627\u0644\u0627\u062A \u0627\u0644\u0645\u0643\u062B\u0641\u0629 \u0630\u0627\u062A \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0648\u062A\u0631\u064A\u0629\u060C \u0648\u063A\u064A\u0631\u0647\u0627 \u0645\u0646 \u062D\u0627\u0644\u0627\u062A \u0627\u0644\u0633\u0648\u0627\u0626\u0644 \u0627\u0644\u0643\u0645\u0648\u0645\u064A\u0629 \u0627\u0644\u0645\u0631\u062A\u0628\u0637\u0629 \u0628\u0642\u0648\u0629. \u0641\u064A \u0627\u0644\u062F\u064A\u0646\u0627\u0645\u064A\u0643\u0627\u060C \u062C\u0645\u064A\u0639 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u062F\u064A\u0646\u0627\u0645\u064A\u0643\u064A\u0629 \u0627\u0644\u0645\u0633\u062A\u0645\u0631\u0629 \u0641\u064A \u0627\u0644\u0632\u0645\u0646\u060C \u0645\u0639 \u0636\u0648\u0636\u0627\u0621 \u0648\u0628\u062F\u0648\u0646\u0647\u0627\u060C \u0647\u064A \u0646\u0638\u0631\u064A\u0627\u062A \u0645\u062C\u0627\u0644\u0627\u062A \u0643\u0645\u064A\u0629 \u0637\u0648\u0628\u0648\u0644\u0648\u062C\u064A\u0629 \u0645\u0646 \u0646\u0648\u0639 \u0648\u064A\u062A\u064A\u0646 \u0648\u062A\u0634\u0645\u0644 \u0638\u0627\u0647\u0631\u0629 \u0627\u0644\u0627\u0646\u0647\u064A\u0627\u0631 \u0627\u0644\u062A\u0644\u0642\u0627\u0626\u064A \u0644\u0644\u062A\u0646\u0627\u0638\u0631 \u0627\u0644\u0641\u0627\u0626\u0642 \u0627\u0644\u0637\u0648\u0628\u0648\u0644\u0648\u062C\u064A \u0627\u0644\u0645\u0637\u0627\u0628\u0642 \u0645\u0641\u0627\u0647\u064A\u0645 \u0631\u0627\u0633\u062E\u0629 \u0645\u062B\u0644 \u0627\u0644\u0641\u0648\u0636\u0649 \u0648\u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628 \u0648 1 / \u0641 \u0648\u0627\u0644\u0636\u0648\u0636\u0627\u0621 \u0627\u0644\u0635\u0627\u062E\u0628\u0629 \u0648\u0627\u0644\u062D\u0631\u062C\u064A\u0629 \u0627\u0644\u0645\u0646\u0638\u0645\u0629 \u0630\u0627\u062A\u064A\u064B\u0627"@ar . . . "Una teor\u00EDa topol\u00F3gica cu\u00E1ntica de campo (TTCC), es una teor\u00EDa cu\u00E1ntica de campos (TCC) que calcula invariantes topol\u00F3gicos. Aunque las TTCCs fueron inventadas por los f\u00EDsicos, ellas tambi\u00E9n son de inter\u00E9s matem\u00E1tico, relacionado, entre otras cosas, con la teor\u00EDa de nudos y la teor\u00EDa de tetra-variedades en topolog\u00EDa algebraica y la en geometr\u00EDa algebraica. S. Donaldson, V. Jones, E. Witten y M. Kontsevich, han ganado la Medalla Fields por sus trabajos relacionados con la teor\u00EDa de campos topol\u00F3gica."@es . . . . "Topologische Quantenfeldtheorie"@de . . . . . . . . . . "\uBB3C\uB9AC\uD559\uACFC \uC218\uD559\uC5D0\uC11C \uC704\uC0C1 \uC591\uC790\uC7A5\uB860(\u4F4D\u76F8\u91CF\u5B50\u5834\u8AD6, \uC601\uC5B4: topological quantum field theory, \uC57D\uC790 TQFT)\uC740 \uACC4\uB7C9 \uD150\uC11C\uC5D0 \uC758\uC874\uD558\uC9C0 \uC54A\uB294 \uC591\uC790\uC7A5\uB860\uC774\uB2E4. \uBBF8\uBD84\uAD6C\uC870\uC870\uCC28 \uACE0\uB824\uD558\uC9C0 \uC54A\uB294 \uC704\uC0C1\uB2E4\uC591\uCCB4\uC5D0\uC11C \uD558\uB294 \uAC83\uC740 \uC544\uB2C8\uACE0, \uC815\uD655\uD788\uB294 \uB9AC\uB9CC \uACC4\uB7C9\uC744 \uACE0\uB824\uD558\uC9C0 \uC54A\uB294 \uBBF8\uBD84\uB2E4\uC591\uCCB4\uC704\uC5D0\uC11C \uD558\uBBC0\uB85C \uC704\uC0C1 \uC591\uC790\uC7A5\uB860\uBCF4\uB2E4\uB294 \uBBF8\uBD84 \uC704\uC0C1 \uC591\uC790\uC7A5\uB860\uC774 \uB354 \uC5B4\uC6B8\uB9AC\uB294 \uC774\uB984\uC774\uB2E4. \uC785\uC790 \uBB3C\uB9AC\uD559\uACFC \uB048 \uC774\uB860, \uC751\uC9D1\uBB3C\uC9C8\uBB3C\uB9AC\uD559\uACFC \uB300\uC218\uC801 \uC704\uC0C1\uC218\uD559, \uB9E4\uB4ED \uC774\uB860\uC5D0\uC11C \uC4F0\uC778\uB2E4."@ko . . . "Topological quantum field theory"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "In fisica matematica, una teoria quantistica dei campi topologica o semplicemente teoria dei campi topologica (in sigla TQFT, da topological quantum field theory) \u00E8 una teoria quantistica dei campi che calcola invarianti topologici. Nella fisica della materia condensata, le teorie topologiche dei campi quantistici sono le teorie efficaci a bassa energia degli stati topologicamente ordinati, come gli stati quantistici frazionari di Hall, gli stati condensati string-net e altri stati liquidi quantistici fortemente correlati."@it . . . . . . . . . "\uC704\uC0C1 \uC591\uC790\uC7A5\uB860"@ko . . 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"\u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0645\u062C\u0627\u0644 \u0627\u0644\u0643\u0645\u064A \u0627\u0644\u0637\u0648\u0628\u0648\u0644\u0648\u062C\u064A\u0629"@ar . . . . "Una teor\u00EDa topol\u00F3gica cu\u00E1ntica de campo (TTCC), es una teor\u00EDa cu\u00E1ntica de campos (TCC) que calcula invariantes topol\u00F3gicos. Aunque las TTCCs fueron inventadas por los f\u00EDsicos, ellas tambi\u00E9n son de inter\u00E9s matem\u00E1tico, relacionado, entre otras cosas, con la teor\u00EDa de nudos y la teor\u00EDa de tetra-variedades en topolog\u00EDa algebraica y la en geometr\u00EDa algebraica. S. Donaldson, V. Jones, E. Witten y M. Kontsevich, han ganado la Medalla Fields por sus trabajos relacionados con la teor\u00EDa de campos topol\u00F3gica. En la f\u00EDsica de materia condensada, las teor\u00EDas topol\u00F3gicas cu\u00E1nticas de campo son teor\u00EDas efectivas de baja energ\u00EDa, de estados ordenados topol\u00F3gicos, como estados fraccionario de Efecto Hall cu\u00E1ntico, condensada y otros estados l\u00EDquidos cu\u00E1nticos fuertemente correlacionados."@es . "In fisica matematica, una teoria quantistica dei campi topologica o semplicemente teoria dei campi topologica (in sigla TQFT, da topological quantum field theory) \u00E8 una teoria quantistica dei campi che calcola invarianti topologici. Sebbene queste teorie topologiche siano state inventate dai fisici, sono anche di interesse matematico, essendo legate, tra le altre cose, alla teoria dei nodi e alla teoria delle quadrivariet\u00E0 in topologia algebrica, e alla teoria degli spazi dei moduli in geometria algebrica. Donaldson, Jones, Witten e Koncevi\u010D hanno tutti vinto la medaglia Fields per i loro lavori sulla matematica relativa alle teorie di campo topologiche. Nella fisica della materia condensata, le teorie topologiche dei campi quantistici sono le teorie efficaci a bassa energia degli stati topologicamente ordinati, come gli stati quantistici frazionari di Hall, gli stati condensati string-net e altri stati liquidi quantistici fortemente correlati. In dinamica, tutti i sistemi dinamici a tempo continuo, con e senza rumore, sono teorie di tipo Witten e il fenomeno di rottura spontanea della supersimmetria topologica corrispondente comprende concetti affermati come caos, turbolenza, rumore 1/f e rumore crackling, criticit\u00E0 auto-organizzata, ecc."@it . . . "In gauge theory and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants. Although TQFTs were invented by physicists, they are also of mathematical interest, being related to, among other things, knot theory and the theory of four-manifolds in algebraic topology, and to the theory of moduli spaces in algebraic geometry. Donaldson, Jones, Witten, and Kontsevich have all won Fields Medals for mathematical work related to topological field theory."@en . . . "1122808083"^^ . . "Teoria quantistica dei campi topologica"@it . . . . . . "Die topologische Quantenfeldtheorie (TQFT) ist eine Verbindung der Quantenfeldtheorie mit Topologie, die Ende der 1980er Jahre entstand (Edward Witten, Michael Atiyah). Verbindungen von Quantentheorie zur Topologie hatte es schon vorher gegeben. Wichtige Gr\u00F6\u00DFen der TQFT sind unabh\u00E4ngig von der Metrik der Mannigfaltigkeiten, auf denen die Quantenfelder definiert sind. Sie sind deshalb als quantenfeldtheoretische Modelle von Interesse, die topologische Invarianten der zugrundeliegenden Mannigfaltigkeiten liefern und fanden deshalb auch in der reinen Mathematik Verwendung, zum Beispiel in der Knotentheorie, in der Topologie von vierdimensionalen Mannigfaltigkeiten und in der Theorie von Modulr\u00E4umen in der algebraischen Geometrie. In der Physik wurden sie zum Beispiel als Modell f\u00FCr Quantengravitation betrachtet, aber auch als effektive Feldtheorien in der Festk\u00F6rperphysik, wo topologische Invarianten zum Beispiel beim Quanten-Hall-Effekt von Bedeutung sind."@de . . . . . . . . "443757"^^ . . "Die topologische Quantenfeldtheorie (TQFT) ist eine Verbindung der Quantenfeldtheorie mit Topologie, die Ende der 1980er Jahre entstand (Edward Witten, Michael Atiyah). Verbindungen von Quantentheorie zur Topologie hatte es schon vorher gegeben. Wichtige Gr\u00F6\u00DFen der TQFT sind unabh\u00E4ngig von der Metrik der Mannigfaltigkeiten, auf denen die Quantenfelder definiert sind. Sie sind deshalb als quantenfeldtheoretische Modelle von Interesse, die topologische Invarianten der zugrundeliegenden Mannigfaltigkeiten liefern und fanden deshalb auch in der reinen Mathematik Verwendung, zum Beispiel in der Knotentheorie, in der Topologie von vierdimensionalen Mannigfaltigkeiten und in der Theorie von Modulr\u00E4umen in der algebraischen Geometrie. In der Physik wurden sie zum Beispiel als Modell f\u00FCr Quantengra"@de . . . . . . . . . . . . . . . . . . . . . . . "\u4F4D\u76F8\u7684\u5834\u306E\u7406\u8AD6"@ja . "Teor\u00EDa topol\u00F3gica cu\u00E1ntica de campo"@es . "In gauge theory and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants. Although TQFTs were invented by physicists, they are also of mathematical interest, being related to, among other things, knot theory and the theory of four-manifolds in algebraic topology, and to the theory of moduli spaces in algebraic geometry. Donaldson, Jones, Witten, and Kontsevich have all won Fields Medals for mathematical work related to topological field theory. In condensed matter physics, topological quantum field theories are the low-energy effective theories of topologically ordered states, such as fractional quantum Hall states, string-net condensed states, and other strongly correlated quantum liquid states."@en . . . . . . . . . . . . .