翻訳と辞書
Words near each other
・ Heisdorf, Germany
・ Heise
・ Heisei Chikuhō Railway
・ Heisei College of Health Sciences
・ Heisei College of Music
・ Heisei Fūzoku
・ Heisei International University
・ Heisei Ishingun
・ Heisei no Sato
・ Heisei Ozeki Dam
・ Heisei period
・ Heisei Station
・ Heisei Ultra Seven
・ Heisenberg
・ Heisenberg cut
Heisenberg group
・ Heisenberg limit
・ Heisenberg model
・ Heisenberg model (quantum)
・ Heisenberg picture
・ Heisenberg's entryway to matrix mechanics
・ Heisenberg's microscope
・ Heisenberg-Langevin equation
・ Heisenbug
・ Heiser
・ Heiser Ridge
・ Heiser, Rosenfeld, and Strauss Buildings
・ Heisey
・ Heisey Glass Company
・ Heisey House


Dictionary Lists
翻訳と辞書 辞書検索 [ 開発暫定版 ]
スポンサード リンク

Heisenberg group : ウィキペディア英語版
Heisenberg group
In mathematics, the Heisenberg group, named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form
::\begin
1 & a & c\\
0 & 1 & b\\
0 & 0 & 1\\
\end
under the operation of matrix multiplication. Elements ''a, b'' and ''c'' can be taken from any commutative ring with identity, often taken to be the ring of real numbers (resulting in the "continuous Heisenberg group") or the ring of integers (resulting in the "discrete Heisenberg group").
The continuous Heisenberg group arises in the description of one-dimensional quantum mechanical systems. More generally, one can consider Heisenberg groups associated to ''n''-dimensional systems, and most generally, to any symplectic vector space.
==The three-dimensional case==
In the three-dimensional case, the product of two Heisenberg matrices is given by:
:\begin
1 & a & c\\
0 & 1 & b\\
0 & 0 & 1\\
\end
\begin
1 & a' & c'\\
0 & 1 & b'\\
0 & 0 & 1\\
\end=
\begin
1 & a+a' & c+c'+ab'\\
0 & 1 & b+b'\\
0 & 0 & 1\\
\end\, .
The neutral element of the Heisenberg group is the identity matrix, and inverses are given by
:\begin
1 & a & c\\
0 & 1 & b\\
0 & 0 & 1\\
\end^=
\begin
1 & -a & ab-c\\
0 & 1 & -b\\
0 & 0 & 1\\
\end\, .
There are several prominent examples of the three-dimensional case.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Heisenberg group」の詳細全文を読む



スポンサード リンク
翻訳と辞書 : 翻訳のためのインターネットリソース

Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.