The need to enforce fermionic antisymmetry in the nuclear many-body problem commonly requires use of single-particle coordinates, defined relative to some fixed origin. To obtain physical operators which nonetheless act on the nuclear many-body system in a Galilean-invariant fashion, thereby avoiding spurious center-of-mass contributions to observables, it is necessary to express these operators with respect to the translational intrinsic frame. Several commonly-encountered operators in nuclear many-body calculations, including the magnetic dipole and electric quadrupole operators (in the impulse approximation) and generators of U(3) and symmetry groups, are bilinear in the coordinates and momenta of the nucleons and, when expressed in intrinsic form, become two-body operators. To work with such operators in a second-quantized many-body calculation, it is necessary to relate three distinct forms: the defining intrinsic-frame expression, an explicitly two-body expression in terms of two-particle relative coordinates, and a decomposition into one-body and separable two-body parts. We establish the relations between these forms, for general (non-scalar and non-isoscalar) operators bilinear in coordinates and momenta.

在核多体问题中需要加强铁离子反对称性通常需要使用相对于某个固定原点定义的单粒子坐标。为了获得仍然以伽利略不变的方式作用于核多体系统的物理算子，从而避免对观测对象的虚假质心贡献，有必要针对平移内在框架表达这些算子。核多体计算中几个常见的算子，包括磁偶极子和电四极子算子（在脉冲近似中）以及U（3）和对称基团在核子的坐标和动量上是双线性的，当以内在形式表示时，它们成为两体算子。为了在第二量化的多体计算中与此类算子配合使用，有必要关联三种不同的形式：定义内在框架表达式，以两粒子相对坐标表示的显式两体表达式以及分解为一主体和可分离的两主体部分。我们为坐标（和动量）中双线性的一般（非标量和非等标量）算子建立了这些形式之间的关系。