"Supersymmetric quantum mechanics"의 두 판 사이의 차이

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-==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
-.$\it F$ 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.
-.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.
-.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

"Supersymmetric quantum mechanics"의 두 판 사이의 차이

2020년 11월 13일 (금) 07:15 판

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