Supersymmetric quantum mechanics - 편집 역사

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@@ 44번째 줄: / 44번째 줄: @@
 [[분류:migrate]]
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q587607 Q587607]

← 이전 판		2020년 12월 28일 (월) 02:50 판
43번째 줄:		43번째 줄:
	* Dana Fine, Stephen Sawin, Path integrals, SUSY QM and the Atiyah-Singer index theorem for twisted Dirac, arXiv:1605.06982 [math-ph], May 23 2016, http://arxiv.org/abs/1605.06982		* Dana Fine, Stephen Sawin, Path integrals, SUSY QM and the Atiyah-Singer index theorem for twisted Dirac, arXiv:1605.06982 [math-ph], May 23 2016, http://arxiv.org/abs/1605.06982
	[[분류:migrate]]		[[분류:migrate]]
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q587607 Q587607]

@@ 1번째 줄: / 1번째 줄: @@
 ==introduction==
 Consider a quantum mechanical system  consisting of a Hilbert (Fock)
-space $\it F$ and Hamiltonian $H$. The system is said to be
+space <math>\it F</math> and Hamiltonian <math>H</math>. The system is said to be
 supersymmetric quantum mechanical (SQM) if
-.$\it F$ has a decomposition ${\it F}={\it F}^B \oplus {\it F}^F$
+.<math>\it F</math> has a decomposition <math>{\it F}={\it F}^B \oplus {\it F}^F</math>
-and states in ${\it F}^B$ and ${\it F}^F$ are called bosonic and
+and states in <math>{\it F}^B</math> and <math>{\it F}^F</math> are called bosonic and
-fermionic states respectively. There is an operator $(-1)^F$ such
+fermionic states respectively. There is an operator <math>(-1)^F</math> such
 that
 \begin{eqnarray}
@@ 12번째 줄: / 12번째 줄: @@
      &&(-1)^F \Psi =-\Psi \ \  if \ \Psi \in {\it F}^F
 \end{eqnarray}
-$F$ and $(-1)^F$ are called fermion number operator and chirality operator.
+<math>F</math> and <math>(-1)^F</math> are called fermion number operator and chirality operator.
-.There are N operators $Q^I$, $I=1,\cdots,N$, such that
+.There are N operators <math>Q^I</math>, <math>I=1,\cdots,N</math>, such that
 \begin{eqnarray}
      Q^I,{Q^I}^\dagger &:&{\it F}^B \rightarrow {\it F}^F ,\\
@@ 20번째 줄: / 20번째 줄: @@
      \left\{ (-1)^F,Q^I\right\}&=&\left\{ (-1)^F,{Q^I}^\dagger\right\}=0
 \end{eqnarray}
-$Q^I$ are called supersymmetry (SUSY) charges or generators.
+<math>Q^I</math> are called supersymmetry (SUSY) charges or generators.
 .The SUSY generators satisfy the general superalgebra condition:
@@ 27번째 줄: / 27번째 줄: @@
         \left\{ Q^I,{Q^J}\right\}&=&\left\{ Q^I,{Q^J}\right\}=0
 \end{eqnarray}
-where $I,J=1,\cdots,N$.
+where <math>I,J=1,\cdots,N</math>.
 A quantum system satisfying the above

← 이전 판	2020년 11월 13일 (금) 15:15 판
1번째 줄:	1번째 줄:
	+	==introduction==
	+	Consider a quantum mechanical system consisting of a Hilbert (Fock)
	+	space $\it F$ and Hamiltonian $H$. The system is said to be
	+	supersymmetric quantum mechanical (SQM) if

	+	1.$\it F$ has a decomposition ${\it F}={\it F}^B \oplus {\it F}^F$
	+	and states in ${\it F}^B$ and ${\it F}^F$ are called bosonic and
	+	fermionic states respectively. There is an operator $(-1)^F$ such
	+	that
	+	\begin{eqnarray}
	+	&&(-1)^F \Psi =\Psi \ \ if \ \Psi \in {\it F}^B \\
	+	&&(-1)^F \Psi =-\Psi \ \ if \ \Psi \in {\it F}^F
	+	\end{eqnarray}
	+	$F$ and $(-1)^F$ are called fermion number operator and chirality operator.
	+
	+	2.There are N operators $Q^I$, $I=1,\cdots,N$, such that
	+	\begin{eqnarray}
	+	Q^I,{Q^I}^\dagger &:&{\it F}^B \rightarrow {\it F}^F ,\\
	+	Q^I,{Q^I}^\dagger &:&{\it F}^F \rightarrow {\it F}^B ,\\
	+	\left\{ (-1)^F,Q^I\right\}&=&\left\{ (-1)^F,{Q^I}^\dagger\right\}=0
	+	\end{eqnarray}
	+	$Q^I$ are called supersymmetry (SUSY) charges or generators.
	+
	+	3.The SUSY generators satisfy the general superalgebra condition:
	+	\begin{eqnarray}
	+	\left\{ Q^I,{Q^J}^\dagger \right\}&=&2 \delta^{IJ} H\\
	+	\left\{ Q^I,{Q^J}\right\}&=&\left\{ Q^I,{Q^J}\right\}=0
	+	\end{eqnarray}
	+	where $I,J=1,\cdots,N$.
	+
	+	A quantum system satisfying the above
	+	conditions is said to have a type N supersymmetry.
	+
	+
	+	==expositions==
	+	* Muhammad Abdul Wasay, Supersymmetric quantum mechanics and topology, http://arxiv.org/abs/1603.07691v1
	+	* van Loon, Mark. “Path Integral Methods in Index Theorems.” arXiv:1509.03063 [math-Ph, Physics:quant-Ph], September 10, 2015. http://arxiv.org/abs/1509.03063.
	+	* Li, Si. “Supersymmetric Quantum Mechanics and Lefschetz Fixed-Point Formula.” arXiv:hep-th/0511101, November 8, 2005. http://arxiv.org/abs/hep-th/0511101.
	+	* Cooper, Fred, Avinash Khare, and Uday Sukhatme. “Supersymmetry and Quantum Mechanics.” Physics Reports 251, no. 5–6 (January 1995): 267–385. doi:10.1016/0370-1573(94)00080-M.
	+
	+	== articles ==
	+
	+	* Dana Fine, Stephen Sawin, Path integrals, SUSY QM and the Atiyah-Singer index theorem for twisted Dirac, arXiv:1605.06982 [math-ph], May 23 2016, http://arxiv.org/abs/1605.06982
	+	[[분류:migrate]]

← 이전 판		2020년 11월 13일 (금) 15:15 판
1번째 줄:		1번째 줄:
−	~~==introduction==~~
−	~~Consider a quantum mechanical system consisting of a Hilbert (Fock)~~
−	~~space $\it F$ and Hamiltonian $H$. The system is said to be~~
−	~~supersymmetric quantum mechanical (SQM) if~~

−	~~1.$\it F$ has a decomposition ${\it F}={\it F}^B \oplus {\it F}^F$~~
−	~~and states in ${\it F}^B$ and ${\it F}^F$ are called bosonic and~~
−	~~fermionic states respectively. There is an operator $(-1)^F$ such~~
−	~~that~~
−	~~\begin{eqnarray}~~
−	~~&&(-1)^F \Psi =\Psi \ \ if \ \Psi \in {\it F}^B \\~~
−	~~&&(-1)^F \Psi =-\Psi \ \ if \ \Psi \in {\it F}^F~~
−	~~\end{eqnarray}~~
−	~~$F$ and $(-1)^F$ are called fermion number operator and chirality operator.~~
−
−	~~2.There are N operators $Q^I$, $I=1,\cdots,N$, such that~~
−	~~\begin{eqnarray}~~
−	~~Q^I,{Q^I}^\dagger &:&{\it F}^B \rightarrow {\it F}^F ,\\~~
−	~~Q^I,{Q^I}^\dagger &:&{\it F}^F \rightarrow {\it F}^B ,\\~~
−	~~\left\{ (-1)^F,Q^I\right\}&=&\left\{ (-1)^F,{Q^I}^\dagger\right\}=0~~
−	~~\end{eqnarray}~~
−	~~$Q^I$ are called supersymmetry (SUSY) charges or generators.~~
−
−	~~3.The SUSY generators satisfy the general superalgebra condition:~~
−	~~\begin{eqnarray}~~
−	~~\left\{ Q^I,{Q^J}^\dagger \right\}&=&2 \delta^{IJ} H\\~~
−	~~\left\{ Q^I,{Q^J}\right\}&=&\left\{ Q^I,{Q^J}\right\}=0~~
−	~~\end{eqnarray}~~
−	~~where $I,J=1,\cdots,N$.~~
−
−	~~A quantum system satisfying the above~~
−	~~conditions is said to have a type N supersymmetry.~~
−
−
−	~~==expositions==~~
−	* Muhammad Abdul Wasay, Supersymmetric quantum mechanics and topology, http://arxiv.org/abs/1603.07691v1
−	* van Loon, Mark. “Path Integral Methods in Index Theorems.” arXiv:1509.03063 [math-Ph, Physics:quant-Ph], September 10, 2015. http://arxiv.org/abs/1509.03063.
−	* Li, Si. “Supersymmetric Quantum Mechanics and Lefschetz Fixed-Point Formula.” arXiv:hep-th/0511101, November 8, 2005. http://arxiv.org/abs/hep-th/0511101.
−	* Cooper, Fred, Avinash Khare, and Uday Sukhatme. “Supersymmetry and Quantum Mechanics.” Physics Reports 251, no. 5–6 (January 1995): 267–385. doi:10.1016/0370-1573(94)00080-M.
−
−	~~== articles ==~~
−
−	* Dana Fine, Stephen Sawin, Path integrals, SUSY QM and the Atiyah-Singer index theorem for twisted Dirac, arXiv:1605.06982 [math-ph], May 23 2016, http://arxiv.org/abs/1605.06982

← 이전 판	2020년 11월 16일 (월) 17:53 판
(차이 없음)

← 이전 판		2016년 6월 2일 (목) 06:13 판
38번째 줄:		38번째 줄:
	* Li, Si. “Supersymmetric Quantum Mechanics and Lefschetz Fixed-Point Formula.” arXiv:hep-th/0511101, November 8, 2005. http://arxiv.org/abs/hep-th/0511101.		* Li, Si. “Supersymmetric Quantum Mechanics and Lefschetz Fixed-Point Formula.” arXiv:hep-th/0511101, November 8, 2005. http://arxiv.org/abs/hep-th/0511101.
	* Cooper, Fred, Avinash Khare, and Uday Sukhatme. “Supersymmetry and Quantum Mechanics.” Physics Reports 251, no. 5–6 (January 1995): 267–385. doi:10.1016/0370-1573(94)00080-M.		* Cooper, Fred, Avinash Khare, and Uday Sukhatme. “Supersymmetry and Quantum Mechanics.” Physics Reports 251, no. 5–6 (January 1995): 267–385. doi:10.1016/0370-1573(94)00080-M.
		+
		+	== articles ==
		+
		+	* Dana Fine, Stephen Sawin, Path integrals, SUSY QM and the Atiyah-Singer index theorem for twisted Dirac, arXiv:1605.06982 [math-ph], May 23 2016, http://arxiv.org/abs/1605.06982

@@ 34번째 줄: / 34번째 줄: @@
 ==expositions==
 * van Loon, Mark. “Path Integral Methods in Index Theorems.” arXiv:1509.03063 [math-Ph, Physics:quant-Ph], September 10, 2015. http://arxiv.org/abs/1509.03063.
 * Li, Si. “Supersymmetric Quantum Mechanics and Lefschetz Fixed-Point Formula.” arXiv:hep-th/0511101, November 8, 2005. http://arxiv.org/abs/hep-th/0511101.
 * Cooper, Fred, Avinash Khare, and Uday Sukhatme. “Supersymmetry and Quantum Mechanics.” Physics Reports 251, no. 5–6 (January 1995): 267–385. doi:10.1016/0370-1573(94)00080-M.

← 이전 판		2015년 12월 20일 (일) 14:48 판
2번째 줄:		2번째 줄:
	* van Loon, Mark. “Path Integral Methods in Index Theorems.” arXiv:1509.03063 [math-Ph, Physics:quant-Ph], September 10, 2015. http://arxiv.org/abs/1509.03063.		* van Loon, Mark. “Path Integral Methods in Index Theorems.” arXiv:1509.03063 [math-Ph, Physics:quant-Ph], September 10, 2015. http://arxiv.org/abs/1509.03063.
	* Li, Si. “Supersymmetric Quantum Mechanics and Lefschetz Fixed-Point Formula.” arXiv:hep-th/0511101, November 8, 2005. http://arxiv.org/abs/hep-th/0511101.		* Li, Si. “Supersymmetric Quantum Mechanics and Lefschetz Fixed-Point Formula.” arXiv:hep-th/0511101, November 8, 2005. http://arxiv.org/abs/hep-th/0511101.
		+	* Cooper, Fred, Avinash Khare, and Uday Sukhatme. “Supersymmetry and Quantum Mechanics.” Physics Reports 251, no. 5–6 (January 1995): 267–385. doi:10.1016/0370-1573(94)00080-M.