Operator calculus and invertible clifford appell systems: Theory and application to the n-particle fermion algebra

Schott R.; Staples G.S.

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Operator calculus and invertible clifford appell systems: Theory and application to the n-particle fermion algebra

机译：算子微积分和可逆的悬崖积分系统：n粒子费米子代数的理论与应用

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Motivated by evolution equations on Clifford algebras and illustrated with the n-particle fermion algebra, a theory of invertible left- and right-Appell systems is developed for Clifford algebras of an arbitrary quadratic form. This work extends and clarifies the authors' earlier work on Clifford Appell systems, operator calculus, and operator homology/cohomology. A direct connection is also shown between blade factorization algorithms and the construction of Appell systems in these algebras.

机译：受Clifford代数上的演化方程激励并用n粒子费米子代数进行说明，为任意二次形式的Clifford代数建立了左右可逆Appell系统理论。这项工作扩展并阐明了作者先前在Clifford Appell系统，算子微积分和算子同源性/同调性方面的工作。在这些代数中，刀片分解算法与Appell系统的构造之间也显示了直接联系。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2013年第1期|共23页
作者
Schott R.; Staples G.S.;
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正文语种 eng
中图分类物理学;
关键词
Appell systems; Clifford algebras; Fermions;

机译：Appell系统;Clifford代数;Ferrions;

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专利

1. Operator calculus and invertible clifford appell systems: Theory and application to the n-particle fermion algebra [J] . Schott R., Staples G.S. Infinite dimensional analysis, quantum probability, and related topics . 2013,第1期

机译：算子微积分和可逆的悬崖积分系统：n粒子费米子代数的理论与应用
2. q-deformed W-ALGEBRA from q-fermion oscillators and the algebraic structure of vertex operators in 2D string theory [J] . Parthasarathy R. Modern Physics Letters, A . 2002,第7期

机译：q费米子振荡器产生的q变形W-ALGEBRA和二维弦论中顶点算子的代数结构
3. Theory of Integral Operators in Parametric Clifford Type Algebras [J] . Vanegas Judith, Vargas Franklin Complex analysis and operator theory . 2020,第1期

机译：参数克利福德型代数中积分运算符的理论
4. Higher order exterior calculus, generalized Clifford algebras and gauge theories [C] . V.Abramov International Conference on Clifford Analysis, Its Applications and Related Topics: In honour of Professor Loo-keng Hua at the occasion of his 90th Birthday August 1-6, 2000 Beijing, People's Republic of China . 2000

机译：高阶外部演算，广义Clifford代数和规范理论
5. Bessel-Clifford operators and the generalized fractional calculus. [D] . Cabrera Suarez, Francisco Simeon. 2001

机译：贝塞尔-克利福德算子和广义分数演算。
6. ON THE UNIFICATION OF THE CALCULUS OF VARIATIONS AND THE THEORY OF MONOTONE NONLINEAR OPERATORS IN BANACH SPACES [O] . Felix E. Browder 1966

机译：Banach空间中变量的计算统一和单调非线性算子理论。
7. Operator calculus and invertible Clifford Appell systems: theory and application to the n-particle fermion algebra [O] . Schott, René, Staples, G. Stacey 2013

机译：算子演算与可逆Clifford Appell系统：n粒子费米子代数的理论与应用
8. Complex Number and Other Extensions to the Clifford Algebra with an Application to the Theory of Continued Fractions [R] . Wynn, P. 1966

机译：Clifford代数的复数和其他扩张及其在连续分数理论中的应用

Operator calculus and invertible clifford appell systems: Theory and application to the n-particle fermion algebra

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