https://pzhou.org/ 2026-08-18T04:34:49+00:00 https://pzhou.org/ https://pzhou.org/lib/tpl/dokuwiki/images/favicon.ico text/html 2023-06-25T15:53:22+00:00 Anonymous (anonymous@undisclosed.example.com) https://pzhou.org/cheatsheets/bargmann-fock?rev=1687708402&do=diff Bargmann-Fock space See <https://arxiv.org/pdf/1604.06655.pdf>, section 1.2 for the circle bundle setup and section 10. text/html 2023-06-25T15:53:22+00:00 Anonymous (anonymous@undisclosed.example.com) https://pzhou.org/cheatsheets/start?rev=1687708402&do=diff Cheat Sheets I am losing my memories, so here is my quick look up place. text/html 2023-06-25T15:53:22+00:00 Anonymous (anonymous@undisclosed.example.com) https://pzhou.org/cheatsheets/symplectic-contact-manifold?rev=1687708402&do=diff Symplectic and Contact manifolds Let's follow the reference of EES (Ekholm-Etnyre-Sabloff). The standard contact form on $\R^3$ is $dz - ydx$. Example of $\C$ Our basic symplectic example is $\C$, where we have $$ \omega = dx \wedge dy, \; J(\d_x) = \d_y \; g(v,v) = \omega(Jv,v) \geq 0. $$