. . . . . . . . . . . "Struttura di spin"@it . "In matematica, e in particolare in geometria differenziale, una struttura di spin definita su una variet\u00E0 riemanniana orientabile (M, g) consente di definire i fibrati spinoriali associati, dando origine alla nozione di campo spinoriale. Le strutture di spin hanno ampie applicazioni in fisica matematica, in particolare nella teoria quantistica dei campi in cui sono un ingrediente essenziale nella definizione di qualsiasi teoria con fermioni privi di carica. Sono anche di interesse puramente matematico in geometria differenziale, topologia algebrica e . Costituiscono le basi per la geometria di spin."@it . . . . . . . . "\uBBF8\uBD84\uC704\uC0C1\uC218\uD559\uC5D0\uC11C \uC2A4\uD540 \uB2E4\uC591\uCCB4(spin\u591A\u6A23\u9AD4, \uC601\uC5B4: spin manifold)\uB294 \uC2A4\uD53C\uB108\uC7A5\uC744 \uC815\uC758\uD560 \uC218 \uC788\uB294 \uB2E4\uC591\uCCB4\uB2E4. \uC989, \uC9C1\uAD50 \uD2C0\uB2E4\uBC1C \uC744 \uC774\uC911 \uD53C\uBCF5 \uACF5\uAC04 \uC5D0 \uB300\uD558\uC5EC \uC801\uC808\uD788 \uC8FC\uB2E4\uBC1C \uC73C\uB85C \uD655\uC7A5\uD560 \uC218 \uC788\uB294 \uAC00\uD5A5 (\uC900) \uB9AC\uB9CC \uB2E4\uC591\uCCB4\uB2E4."@ko . . . . . . "Structure spinorielle"@fr . "\uC2A4\uD540 \uB2E4\uC591\uCCB4"@ko . . . . . . . . . . . . . . . . . . . . . . . . . . . . "2844303"^^ . . . . "29807"^^ . . . . . . . "In matematica, e in particolare in geometria differenziale, una struttura di spin definita su una variet\u00E0 riemanniana orientabile (M, g) consente di definire i fibrati spinoriali associati, dando origine alla nozione di campo spinoriale."@it . "1113944806"^^ . . "\u5FAE\u5206\u5E7E\u4F55\u5B66\u306B\u304A\u3044\u3066\u3001\u5411\u304D\u4ED8\u3051\u53EF\u80FD\u30EA\u30FC\u30DE\u30F3\u591A\u69D8\u4F53 (M, g) \u4E0A\u306E\u30B9\u30D4\u30F3\u69CB\u9020\uFF08\u30B9\u30D4\u30F3\u3053\u3046\u305E\u3046\u3001\u82F1: spin structure\uFF09\u306F\u3001\u4ED8\u968F\u3059\u308B\u306E\u5B9A\u7FA9\u3092\u53EF\u80FD\u306B\u3057\u3001\u5FAE\u5206\u5E7E\u4F55\u5B66\u306B\u304A\u3051\u308B\u30B9\u30D4\u30CE\u30EB\u306E\u6982\u5FF5\u3092\u751F\u3058\u308B\u3002 \u6570\u7406\u7269\u7406\u5B66\u3001\u7279\u306B\u5834\u306E\u91CF\u5B50\u8AD6\u3078\u5E83\u304F\u5FDC\u7528\u3055\u308C\u3001\u96FB\u8377\u3092\u6301\u305F\u306A\u3044\u30D5\u30A7\u30EB\u30DF\u30AA\u30F3\u306B\u95A2\u3059\u308B\u4EFB\u610F\u306E\u7406\u8AD6\u306E\u5B9A\u7FA9\u306B\u30B9\u30D4\u30F3\u69CB\u9020\u306F\u5FC5\u9808\u3067\u3042\u308B\u3002\u7D14\u7C8B\u6570\u5B66\u7684\u306B\u3082\u3001\u5FAE\u5206\u5E7E\u4F55\u5B66\u3084\u4EE3\u6570\u7684\u4F4D\u76F8\u5E7E\u4F55\u5B66\u3001K-\u7406\u8AD6\u306A\u3069\u306B\u65BC\u3044\u3066\u30B9\u30D4\u30F3\u69CB\u9020\u306F\u8208\u5473\u306E\u5BFE\u8C61\u3067\u3042\u308B\u3002\u30B9\u30D4\u30F3\u69CB\u9020\u306F\u306B\u5BFE\u3059\u308B\u57FA\u790E\u4ED8\u3051\u3092\u6210\u3059\u3002"@ja . . . . "\u30B9\u30D4\u30F3\u69CB\u9020"@ja . . . "In differential geometry, a spin structure on an orientable Riemannian manifold (M, g) allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry. Spin structures have wide applications to mathematical physics, in particular to quantum field theory where they are an essential ingredient in the definition of any theory with uncharged fermions. They are also of purely mathematical interest in differential geometry, algebraic topology, and K theory. They form the foundation for spin geometry."@en . . . . . . . . . . . . . "Spin structure"@en . . . . . . . . . . . . "En g\u00E9om\u00E9trie diff\u00E9rentielle, il est possible de d\u00E9finir sur certaines vari\u00E9t\u00E9s riemanniennes la notion de structure spinorielle (qui se d\u00E9cline en structures Spin ou Spinc), \u00E9tendant ainsi les consid\u00E9rations alg\u00E9briques sur le groupe spinoriel et les spineurs. En termes imag\u00E9s, il s'agit de trouver, dans le cadre des \u00AB espaces courbes \u00BB, une g\u00E9om\u00E9trie \u00AB cach\u00E9e \u00BB \u00E0 l\u2019\u0153uvre derri\u00E8re les concepts g\u00E9om\u00E9triques ordinaires. On peut aussi y voir une g\u00E9n\u00E9ralisation de la notion d'orientabilit\u00E9 et de changement d'orientation \u00E0 une forme d'\u00AB orientabilit\u00E9 d'ordre sup\u00E9rieur \u00BB. Comme l'orientabilit\u00E9, la pr\u00E9sence de structures spinorielles n'est pas universelle mais se heurte \u00E0 des obstructions qui peuvent \u00EAtre formul\u00E9es en termes de classes caract\u00E9ristiques."@fr . . . . . . . . . . . . . . . . . . . . . . . . . . . "\u5FAE\u5206\u5E7E\u4F55\u5B66\u306B\u304A\u3044\u3066\u3001\u5411\u304D\u4ED8\u3051\u53EF\u80FD\u30EA\u30FC\u30DE\u30F3\u591A\u69D8\u4F53 (M, g) \u4E0A\u306E\u30B9\u30D4\u30F3\u69CB\u9020\uFF08\u30B9\u30D4\u30F3\u3053\u3046\u305E\u3046\u3001\u82F1: spin structure\uFF09\u306F\u3001\u4ED8\u968F\u3059\u308B\u306E\u5B9A\u7FA9\u3092\u53EF\u80FD\u306B\u3057\u3001\u5FAE\u5206\u5E7E\u4F55\u5B66\u306B\u304A\u3051\u308B\u30B9\u30D4\u30CE\u30EB\u306E\u6982\u5FF5\u3092\u751F\u3058\u308B\u3002 \u6570\u7406\u7269\u7406\u5B66\u3001\u7279\u306B\u5834\u306E\u91CF\u5B50\u8AD6\u3078\u5E83\u304F\u5FDC\u7528\u3055\u308C\u3001\u96FB\u8377\u3092\u6301\u305F\u306A\u3044\u30D5\u30A7\u30EB\u30DF\u30AA\u30F3\u306B\u95A2\u3059\u308B\u4EFB\u610F\u306E\u7406\u8AD6\u306E\u5B9A\u7FA9\u306B\u30B9\u30D4\u30F3\u69CB\u9020\u306F\u5FC5\u9808\u3067\u3042\u308B\u3002\u7D14\u7C8B\u6570\u5B66\u7684\u306B\u3082\u3001\u5FAE\u5206\u5E7E\u4F55\u5B66\u3084\u4EE3\u6570\u7684\u4F4D\u76F8\u5E7E\u4F55\u5B66\u3001K-\u7406\u8AD6\u306A\u3069\u306B\u65BC\u3044\u3066\u30B9\u30D4\u30F3\u69CB\u9020\u306F\u8208\u5473\u306E\u5BFE\u8C61\u3067\u3042\u308B\u3002\u30B9\u30D4\u30F3\u69CB\u9020\u306F\u306B\u5BFE\u3059\u308B\u57FA\u790E\u4ED8\u3051\u3092\u6210\u3059\u3002"@ja . . . . . "En g\u00E9om\u00E9trie diff\u00E9rentielle, il est possible de d\u00E9finir sur certaines vari\u00E9t\u00E9s riemanniennes la notion de structure spinorielle (qui se d\u00E9cline en structures Spin ou Spinc), \u00E9tendant ainsi les consid\u00E9rations alg\u00E9briques sur le groupe spinoriel et les spineurs. En termes imag\u00E9s, il s'agit de trouver, dans le cadre des \u00AB espaces courbes \u00BB, une g\u00E9om\u00E9trie \u00AB cach\u00E9e \u00BB \u00E0 l\u2019\u0153uvre derri\u00E8re les concepts g\u00E9om\u00E9triques ordinaires. On peut aussi y voir une g\u00E9n\u00E9ralisation de la notion d'orientabilit\u00E9 et de changement d'orientation \u00E0 une forme d'\u00AB orientabilit\u00E9 d'ordre sup\u00E9rieur \u00BB. Comme l'orientabilit\u00E9, la pr\u00E9sence de structures spinorielles n'est pas universelle mais se heurte \u00E0 des obstructions qui peuvent \u00EAtre formul\u00E9es en termes de classes caract\u00E9ristiques. Quand elles existent, ces structures jouent un r\u00F4le important en g\u00E9om\u00E9trie diff\u00E9rentielle et en physique th\u00E9orique. Elles permettent notamment d'introduire l' (en), sorte de racine carr\u00E9e du laplacien, ou les invariants de Seiberg-Witten pour les vari\u00E9t\u00E9s orient\u00E9es de dimension 4."@fr . "In differential geometry, a spin structure on an orientable Riemannian manifold (M, g) allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry. Spin structures have wide applications to mathematical physics, in particular to quantum field theory where they are an essential ingredient in the definition of any theory with uncharged fermions. They are also of purely mathematical interest in differential geometry, algebraic topology, and K theory. They form the foundation for spin geometry."@en . . . "\uBBF8\uBD84\uC704\uC0C1\uC218\uD559\uC5D0\uC11C \uC2A4\uD540 \uB2E4\uC591\uCCB4(spin\u591A\u6A23\u9AD4, \uC601\uC5B4: spin manifold)\uB294 \uC2A4\uD53C\uB108\uC7A5\uC744 \uC815\uC758\uD560 \uC218 \uC788\uB294 \uB2E4\uC591\uCCB4\uB2E4. \uC989, \uC9C1\uAD50 \uD2C0\uB2E4\uBC1C \uC744 \uC774\uC911 \uD53C\uBCF5 \uACF5\uAC04 \uC5D0 \uB300\uD558\uC5EC \uC801\uC808\uD788 \uC8FC\uB2E4\uBC1C \uC73C\uB85C \uD655\uC7A5\uD560 \uC218 \uC788\uB294 \uAC00\uD5A5 (\uC900) \uB9AC\uB9CC \uB2E4\uC591\uCCB4\uB2E4."@ko . . . . . . . . .