"Heisenberg group and Heisenberg algebra"의 두 판 사이의 차이

2009년 8월 13일 (목) 01:43 판

start with a Lattice \(<\cdot,\cdot>\)
make a vector space from it
Construct a Loop algbera
\(A\otimes\mathbb{C}[t,t^{-1}]\oplus\mathbb{C}c\)
\(\alpha(m)=\alpha\otimes t^m\)
Give a bracket
\([\alpha(m),\beta(n)]=m\delta_{m,-n}<\alpha,\beta>c\)
add a derivation \(d\)
\(d(\alpha(n))=n\alpha(n)\)
\(d(c)=0\)
define a Lie bracket
\([d,x]=d(x)\)

@@ 3번째 줄: / 3번째 줄: @@
 *  start with a Lattice <math><\cdot,\cdot></math><br>
 *  make a vector space from it<br>
-* <math>[\alpha(m),\beta(n)]=m\delta_{m,-n}<\alpha,\beta>c</math><br>
+*  Construct a Loop algbera<br><math>A\otimes\mathbb{C}[t,t^{-1}]\oplus\mathbb{C}c</math><br><math>\alpha(m)=\alpha\otimes t^m</math><br>
+*  Give a bracket <br><math>[\alpha(m),\beta(n)]=m\delta_{m,-n}<\alpha,\beta>c</math><br>
 *  add a derivation <math>d</math><br><math>d(\alpha(n))=n\alpha(n)</math><br><math>d(c)=0</math><br>
 *  define a Lie bracket<br><math>[d,x]=d(x)</math><br>
+<h5 style="line-height: 2em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;">relation to quantum mechanics</h5>
+*   the position operators and momentum operators<br>