実数の量子化 ― 量子重力理論へのひとつのアプローチ ―

URI http://harp.lib.hiroshima-u.ac.jp/it-hiroshima/metadata/12145
ファイル
タイトル
実数の量子化 ― 量子重力理論へのひとつのアプローチ ―
別タイトル
Quantization of Real Numbers ― An Approach to Quantum Gravity Theory ―
著者
氏名 鈴木 貴
ヨミ スズキ タカシ
別名 Suzuki Takashi
キーワード
Quantum real numbers
Deformation quantization
Noncommutative geometry
Super-space
抄録

Towards a quantum theory of gravity, this paper presents a possible quantization of real numbers. The procedure to obtain a quantum real is as follows: We first prepare two algebras on the base space R, a function algebra H(R) and the Heisenberg algebra A(R) as the operator algebra on H(R). According to the scheme of, so-called, the deformation quantization, we obtain the deformed Heisenberg algebra Aq(R) with the deformation parameter q ∈ and, then, construct the deformed function algebra Hq(R) on which Aq(R) acts . The base space R introduced formally here is regarded as the quantum real numbers. In particular, we focus on the case where the parameter q is the N-th root of unity and obtain the deformed algebras Aq(R(N)); Hq(R(N)). Here, R(N) := R|qN=1 is proposed as the conclusive quantum real numbers. We further investigate the structure of R(N) and show that R(N) is isomorphic to the space Rq(N):= R×G(N) where the extra dimension G(N) is (para-)Grassmann space. Our conclusion is that the quantum real numbers Rq(N) is just the (para-)superspace.

掲載雑誌名
広島工業大学紀要. 研究編
51
開始ページ
49
終了ページ
59
出版年月日
2017-02
出版者
広島工業大学
ISSN
1346-9975
NCID
AA11599110
本文言語
日本語
資料タイプ
紀要論文
著者版フラグ
出版社版
区分
it-hiroshima