发表机构
Bogoliubov Laboratory of Theoretical Physics, JINR; Moscow Institute of Physics and Technology（约飞联合核子研究所理论物理实验室; 莫斯科物理技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在调和超空间方法中构造4D N=2超对称代数的卡西米尔算子，给出超同位旋等算子表达式，还构造无质量情形相关的超螺旋度算子并求其本征值。
AI 中文摘要
我们在调和超空间方法中构造了4D N=2超对称代数的卡西米尔算子，并基于解析基给出了它们的显式表达式。具体而言，超同位旋算子CI由新的“长”调和导数∇±±、∇0表示为CI=1/4(∇0)² + 1/2{∇++,∇--}。这些导数包含带逆达朗贝尔算子□⁻¹的非定域项，且满足修正的SU(2)代数关系，其中∇0在解析超场上的本征值相对于标准U(1)调和荷偏移了-2。我们还构造了与无质量情形（□=0）相关的N=2超螺旋度和超同位旋螺旋度算子，并针对几个有启发性的4D N=2超场理论示例求出了它们的本征值。
英文摘要
We construct Casimir operators of $4D, \,\mathcal{N}=2$ supersymmetry algebra in the harmonic superspace approach, and provide the explicit expressions for them in terms of covariant derivatives in the analytic basis. Specifically, the superisospin operator $C_I$ is expressed in terms of new 'long' harmonic derivatives $\nabla^{\pm\pm}, \nabla^0$ as $C_I = \frac{1}{4}\left(\nabla^0\right)^2 + \frac{1}{2}\left\{\nabla^{++},\nabla^{--}\right\}$. These derivatives involve non-local terms with the inverse Box operator $\Box^{-1}$ and satisfy modified $SU(2)$ algebra relations in which the eigenvalues of $\nabla^0$ on analytic superfields are shifted by -2 relative to the standard $U(1)$ harmonic charges. We also construct $\mathcal{N}=2$ superhelicity and super-isohelicity operators relevant to the massless case (with vanishing $\Box$) and find their eigenvalues for few instructive examples of $4D, \,\mathcal{N}=2$ superfield theories.
Comments0 + 38 pages, typos corrected
