Multipole expansion at the level of the action
Multipole expansion at the level of the action
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动作层面的多极扩展
DOI：
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发表时间：
2012
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通讯作者：
A. Ross
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文献类型：
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作者：
A. Ross
长波辐射源自然地被有效场论（EFT）描述，它采取多极展开的形式。它的作用是由导数展开给出的，其中高阶项被源尺寸与波长之比的幂所抑制。为了确定EFT的Wilson系数，即多极矩，需要线性源项作用与EFT作用的多极展开形式之间的映射。本文通过Taylor展开源项上的场，将其分解为对称的迹自由张量，形成旋转群的不可约表示，从而对所有阶进行多极展开。我们在作用的层面上进行研究，得到了多极展开中所有阶的作用，以及标量场、电磁场和线性化重力场的多极矩的精确表达式。对于后两种情况，我们的结果显然是规范不变的。我们还给出了多极膨胀中各阶的能量通量和辐射场（规范相关）的表达式。线性化重力的结果是EFT框架NRGR的一个组成部分，将大大简化NRGR辐射部分引力波观测值的未来计算。
Sources of long wavelength radiation are naturally described by an effective field theory (EFT) which takes the form of a multipole expansion. Its action is given by a derivative expansion where higher order terms are suppressed by powers of the ratio of the size of the source over the wavelength. In order to determine the Wilson coefficients of the EFT, i.e. the multipole moments, one needs the mapping between a linear source term action and the multipole expansion form of the action of the EFT. In this paper we perform the multipole expansion to all orders by Taylor expanding the field in the source term and then decomposing the action into symmetric trace free tensors which form irreducible representations of the rotation group. We work at the level of the action, and we obtain the action to all orders in the multipole expansion and the exact expressions for the multipole moments for a scalar field, electromagnetism and linearized gravity. Our results for the latter two cases are manifestly gauge invariant. We also give expressions for the energy flux and the (gauge dependent) radiation field to all orders in the multipole expansion. The results for linearized gravity are a component of the EFT framework NRGR and will greatly simplify future calculations of gravitational wave observables in the radiation sector of NRGR.