具有奇Clifford参数和超对称性的超群的修正Leibniz规则
On Supergroups with Odd Clifford Parameters and Supersymmetry with Modified Leibniz Rule
摘要：
研究了用奇Clifford参数代替Grassmann参数的超群.与非反对易超对称性的连接进行了讨论。引入了奇Clifford变量的Berezin类演算。导出了奇Clifford变量超群的费米子协变导数。超对称量子力学的应用。当费米子协变导数不服从分次莱布尼兹性质时，原超对称理论会发生变形。最简单的非平凡例子是N=2的SQM，它有一个实$(1,2,1)$多重态和一个立方势。行动是真实的。根据变形的整体符号（“欧几里德”或“洛伦兹”），在求解辅助场的运动方程时会遇到Bender-Boettcher伪厄米哈密顿量。我们的框架与超对称的德林费尔德扭曲变形的一个可能的连接被指出。
英文摘要：
We investigate supergroups with Grassmann parameters replaced by odd Clifford parameters. The connection with non-anticommutative supersymmetry is discussed. A Berezin-like calculus for odd Clifford variables is introduced. Fermionic covariant derivatives for supergroups with odd Clifford variables are derived. Applications to supersymmetric quantum mechanics are made. Deformations of the original supersymmetric theories are encountered when the fermionic covariant derivatives do not obey the graded Leibniz property. The simplest non-trivial example is given by the N=2 SQM with a real $(1,2,1)$ multiplet and a cubic potential. The action is real. Depending on the overall sign ("Euclidean" or "Lorentzian") of the deformation, a Bender-Boettcher pseudo-hermitian hamiltonian is encountered when solving the equation of motion of the auxiliary field. A possible connection of our framework with the Drinfeld twist deformation of supersymmetry is pointed out.
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