论文标题
球体路径积分的纲要
A Compendium of Sphere Path Integrals
论文作者
论文摘要
我们研究了$ s^{d+1} $在$ s^{d+1} $上的明显协变量和局部1循环路径积分，用于一般大规模，换档对称性和（部分）无质量的完全对称张量张量$ s \ geq 0 $在任何维度中的$ d \ degeq 2 $。在审查了Spin $ s = 1,2 $的无质量领域的案例之后，我们为任意整数旋转$ S \ geq 1 $的无质量字段的路径积分提供了详细的推导。遵循灯 - 旋转负形式模式的标准过程，我们发现Polchinski相位的较高自旋类似物对于任何整数旋转$ s \ geq 2 $。低自旋（$ s = 0,1,2 $）的派生也明确地进行了大规模，移位对称和部分无质量的场。最后，我们为任意整数旋转以及任意整数旋转和深度的部分无质量的旋转和部分无质量的磁场提供一般规定。
We study the manifestly covariant and local 1-loop path integrals on $S^{d+1}$ for general massive, shift-symmetric and (partially) massless totally symmetric tensor fields of arbitrary spin $s\geq 0$ in any dimensions $d\geq 2$. After reviewing the cases of massless fields with spin $s=1,2$, we provide a detailed derivation for path integrals of massless fields of arbitrary integer spins $s\geq 1$. Following the standard procedure of Wick-rotating the negative conformal modes, we find a higher spin analog of Polchinski's phase for any integer spin $s\geq 2$. The derivations for low-spin ($s=0,1,2$) massive, shift-symmetric and partially massless fields are also carried out explicitly. Finally, we provide general prescriptions for general massive and shift-symmetric fields of arbitrary integer spins and partially massless fields of arbitrary integer spins and depths.
