论文标题
（非）在de Sitter空间上严格和部分无质量费米的单位性II：基于spin-3/2和spin-5/2特征模的群体理论特性的解释
(Non-)unitarity of strictly and partially massless fermions on de Sitter space II: an explanation based on the group-theoretic properties of the spin-3/2 and spin-5/2 eigenmodes
论文作者
论文摘要
在我们上一篇文章[Letsios 2023 J. High Energ。物理。 JHEP05（2023）015]，我们表明，严格无质量的Spin-3/2字段以及严格的和部分无质量的Spin-5/2字段，在$ n $ diperional上（$ n $ dimensional（$ n \ geq 3 $ 3 $）de Sitter Spacetime（$ ds_ {n} $）是非独立的。通过简单地观察到与de de Sitter（DS）代数旋转$（n，1）$的单位不可约表示（uir's）之间相对应的表示形式的理论标签与对应于现场理论的eigenmodes空间相对应的表示对应的表示形式的理论标签（UIR''s）之间存在（非）单位性的（非）单位性。在本文中，我们通过研究Spin-3/2和Spin-5/2的（严格/部分无质量的特征）在$ ds_ {n} $（$ n} $ 3 $）上的（$ n \ egq 3 $）上的（$ n \ n} $）上的（$ n \ n} $ ds的（spin-5/2），我们为这一事实提供了技术表示解释。我们的基本工具是对旋转$（n，1）$发电机在本征码空间的作用的检查，从而导致以下发现。对于奇数$ n $，任何DS不变标量产品的均为零。对于$ n> 4 $，任何DS不变标量产品都必须不确定。这引起了正负和负征本素质，它们在旋转$（n，1）$ boosts下相互混合。在$ n = 4 $的情况下，正核行业从负面部门脱离了负面部门，每个部门分别构成了旋转$（4,1）$的UIR。我们的分析广泛利用了张量 - 螺旋球形谐波在$ n $ -sphere（$ s^{n} $）上的分析性延续到$ ds_ {n} $上，并且还引入了代表性理论技术，这些技术是从Half-oddd-odd-odd-ddd-integer-spiner of y Math-odd-oddd-integer-spin of oon $ ds-oddd-integer-spin con y $ ds_ $ ds_ $ ds_} $ ds_ {
In our previous article [Letsios 2023 J. High Energ. Phys. JHEP05(2023)015], we showed that the strictly massless spin-3/2 field, as well as the strictly and partially massless spin-5/2 fields, on $N$-dimensional ($N \geq 3 $) de Sitter spacetime ($dS_{N}$) are non-unitary unless $N=4$. The (non-)unitarity was demonstrated by simply observing that there is a (mis-)match between the representation-theoretic labels that correspond to the Unitary Irreducible Representations (UIR's) of the de Sitter (dS) algebra spin$(N,1)$ and the ones corresponding to the space of eigenmodes of the field theories. In this paper, we provide a technical representation-theoretic explanation for this fact by studying the (non-)existence of positive-definite, dS invariant scalar products for the spin-3/2 and spin-5/2 strictly/partially massless eigenmodes on $dS_{N}$ ($N \geq 3$). Our basic tool is the examination of the action of spin$(N,1)$ generators on the space of eigenmodes, leading to the following findings. For odd $N$, any dS invariant scalar product is identically zero. For even $N > 4$, any dS invariant scalar product must be indefinite. This gives rise to positive-norm and negative-norm eigenmodes that mix with each other under spin$(N,1)$ boosts. In the $N=4$ case, the positive-norm sector decouples from the negative-norm sector and each sector separately forms a UIR of spin$(4,1)$. Our analysis makes extensive use of the analytic continuation of tensor-spinor spherical harmonics on the $N$-sphere ($S^{N}$) to $dS_{N}$ and also introduces representation-theoretic techniques that are absent from the mathematical physics literature on half-odd-integer-spin fields on $dS_{N}$.
