发表机构
Erciyes University（埃尔齐耶斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究对局域四导数对称远平行引力做分支完备的经典自由谱分析，推导其物理谱结构，确定仅两类位点为健康的闵可夫斯基解，揭示张量与标量交换的标度行为。
AI 中文摘要
我们对包含所有纯引力非度规算子且具有宇称偶性的局域对称远平行引力（symmetric teleparallel gravity）开展分支完备的经典自由谱分析，该分析涉及四导数项。经正则化和分部积分后，非线性作用量包含116个独立算子，按$Q^2$、$(\nabla Q)^2$、$Q^2\nabla Q$和$Q^4$的分布分别为5个、13个、29个和69个。在重合规范（coincident gauge）的闵可夫斯基（Minkowski）时空附近，仅前两类算子对二次作用量有贡献，该二次作用量可简化为4个双导数双线型项和5个四导数双线型项。我们将原始系数映射到这个九维基上，构造海森矩阵（Hessian）和动量核（momentum kernel），并对局域线性规范对称性进行分类。无约束的线性微分同胚不变性施加6个独立关系，留下一个三参数族$(A,B,C)$。我们还恢复了TDiff、Weyl、WTDiff及额外的意外对称性分支。通过Barnes–Rivers分解、规范固定、精确求逆和守恒源饱和，物理交换可简化为自旋2因子和标量因子$A+2Cq$与$2A+(3B-2C)q$。一般正则谱包含无质量引力子、一个有质量自旋2态和一个有质量标量，共8个自由度。有质量自旋2的留数必然与健康无质量引力子的留数符号相反。正则分类仅保留GR/STEGR（$A>0$且$B=C=0$）和标量扩展（$A>0$、$B>0$且$C=0$）作为完全健康的闵可夫斯基位点，后者具有3个自由度和混合紫外行为，其中张量交换按$k^{-2}$标度，标量交换按$k^{-4}$标度。因此，在该有限局域度规理论中，完整的四导数张量抑制需要具有相反留数的有限有质量自旋2极点。
英文摘要
We develop a branch-complete classical free-spectrum analysis of local parity-even symmetric teleparallel gravity containing all pure-gravity nonmetricity operators through four derivatives. After canonicalisation and integration by parts, the nonlinear action contains 116 independent operators distributed as $5+13+29+69$ among $Q^2$, $(\nabla Q)^2$, $Q^2\nabla Q$ and $Q^4$. Around Minkowski spacetime in the coincident gauge only the first two sectors contribute to the quadratic action, which reduces to four two-derivative and five four-derivative bilinears. We map the original coefficients to this nine-dimensional basis, construct the Hessian and momentum kernel, and classify local linear gauge symmetries. Unrestricted linearised diffeomorphism invariance imposes six independent relations and leaves a three-parameter family $(A,B,C)$. We also recover TDiff, Weyl, WTDiff and additional accidental symmetry branches. Barnes--Rivers decomposition, gauge fixing, exact inversion and conserved-source saturation reduce the physical exchange to spin-two and scalar factors $A+2Cq$ and $2A+(3B-2C)q$. The generic regular spectrum contains a massless graviton, a massive spin-two state and a massive scalar, with eight degrees of freedom. The massive spin-two residue is necessarily opposite to that of the healthy massless graviton. The regular classification leaves only GR/STEGR, $A>0$ with $B=C=0$, and the scalar extension, $A>0$, $B>0$, $C=0$, as fully healthy Minkowski loci. The latter has three degrees of freedom and mixed ultraviolet behaviour, with tensor exchange scaling as $k^{-2}$ and scalar exchange as $k^{-4}$. Thus, within this finite local metric theory, full four-derivative tensor suppression requires the finite massive spin-two pole with opposite residue.
Comments21 pages, 2 tables
