tag:blogger.com,1999:blog-4352371825685007367.post1751603637806460754..comments2022-03-25T11:26:38.618+09:00Comments on From Mirror Symmetry to Langlands Correspondence: 第七回目数理物理セミナKen Yokoyamahttp://www.blogger.com/profile/05236785937528140451noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-4352371825685007367.post-4065603505442913172013-08-04T17:49:38.475+09:002013-08-04T17:49:38.475+09:004 Aug 2013
板書の中では、時間発展の定義は正しいが、Riemann構造が入っていないと、...4 Aug 2013<br /><br />板書の中では、時間発展の定義は正しいが、Riemann構造が入っていないと、おそらく確率振幅が定義できない.位相だけだとrigidであり、局所自由度がない.<br /><br />John Baez has written various things about this. Briefly, cobordisms should be thought of in terms of time evolution: you have two manifolds which represent space, and a cobordism between them represents time evolution. Of course to be more physically realistic one should put a Lorentzian structure on the cobordism and make the two manifolds spacelike slices, but I guess the point of the adjective "topological" is to ignore these extra details for the sake of mathematical simplicity.<br /><br />Then the functor to Vect is supposed to be a simple version of a functor to Hilb (the category of Hilbert spaces) assigning to a manifold the Hilbert space of states on it, and assigning to a cobordism a linear operator representing time evolution. Again, to be more physically realistic one should demand that the operator be unitary and indeed there is a notion of unitary TQFT (but many TQFTs of interest to mathematicians are not unitary).ennoreply@blogger.comtag:blogger.com,1999:blog-4352371825685007367.post-23140008566280795562012-12-31T11:12:02.471+09:002012-12-31T11:12:02.471+09:0031 Dec. 2012 確率振幅のみに話を限定してトークをしたことは良くなかったと反省している.他...31 Dec. 2012 確率振幅のみに話を限定してトークをしたことは良くなかったと反省している.他に<br /><br />1、境界値<br />2、内積<br />3、(外)微分形式<br />4、Category化との関係(TFTはSymmetric Monoidal Category)<br /><br />の基本的な話をすべきでした.Ken Yokoyamahttps://www.blogger.com/profile/05236785937528140451noreply@blogger.com