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

2009년 9월 10일 (목) 19:32 판

The automorphisms of the Heisenberg group (fixing its center) form the symplectic group

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
\([d,x]=d(x)\)

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+The automorphisms of the Heisenberg group (fixing its center) form the symplectic group
 <h5 style="line-height: 3.428em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">introduction</h5>
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 <h5 style="line-height: 2em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">relation to quantum mechanics</h5>
-*   the position operators and momentum operators<br>
+*   the position operators and momentum operators satisfy the above relation<br>