标题： 自旋依赖的共形不变积分变换 显示英文标题

标题： Spin-dependent conformally invariant integral transform

摘要： 作为Hilbert变换的扩展，该变换表征了时空共形不变积分变换，我们表明，基于Bhabha理论，可以将自旋依赖的共形不变积分变换写成自旋无关积分变换和相应共形群的Casimir算子的乘积。 与通常情况下假设时空平移对称性不同，我们引入了一个内禀动量算子，通过该算子，Casimir算子被证明是时空相关的（自旋-轨道耦合、Pauli-Lubanski伪矢量等）。 我们还表明，被内禀动量算子湮灭的物理态代表一个自旋-s态。 显示英文摘要

摘要： As an extension of the Hilbert transform, which characterizes the spacetime conformally invariant integral transform, we show that, based on the Bhabha theory, a spin-dependent conformally invariant integral transform can be written as a product of the spin-independent integral transform and the Casimir operator of the corresponding conformal group. In contrast to an ordinary context, where spacetime translation symmetry is assumed, we introduce an intrinsic momentum operator, by which the Casimir operator turns out to be spacetime dependent (spin-orbit coupling, Pauli-Lubanski pseudo vector, and the like). We also show that the physical state annihilated by the intrinsic momentum operator represents a spin-s state.