arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2602.14971hep-thgr-qc
收藏

高维中引力S矩阵的单位性

On the Unitarity of the Gravitational S-Matrix in High Dimension

Rutgers University（罗格斯大学）；NHETC（新泽西理论物理中心）

T. Banks

备注：
19 pages, 2 Figures, LaTeX2e
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

研究高维引力S矩阵的单位性，发现其在有限能量窗口内可归一化，但随着能量趋于无穷大，S矩阵在Fock空间中无法保持单位性，需进一步证明其庞加莱不变性。

摘要：

我们论证，在有限能量窗口内，高维（d > 4）引力散射中的最终态是可归一化的相干态，在Fock空间中。然而，当能量窗口中心趋于无穷大时，黑洞物理预测这些态与具有有限粒子数的态正交。由于能量谱测度由庞加莱不变性决定，S矩阵在Fock空间中不能是单位算子，尽管其在Fock空间中有有限矩阵元，并在弦扰动理论的所有阶数中满足微扰单位性。我们识别了BFSS矩阵模型和S矩阵定义作为CFT相关子极限的某些情形，得出相同结论。我们回顾了基于有限数量费米振子量子力学的散射理论，其代数形式上收敛于超庞加莱协变的Awada-Gibbons-Shaw代数，并论证了该代数上的某些极限态满足所有所需物理单位性属性。唯一缺失的成分是证明S矩阵幅本身是庞加莱不变的。我们提供了有说服力的论据，但并未真正证明这一点。

英文摘要：

We argue that for finite energy windows, the final states in gravitational scattering in dimension $d > 4$ are normalizable coherent states in Fock space. However, as the center of the energy window goes to infinity, black hole physics predicts that these states become orthogonal to every state with a finite number of particles. Given that the spectral measure in energy is determined by Poincare invariance, the S-matrix cannot be a unitary operator in Fock space, despite having finite matrix elements in Fock space, and satisfying perturbative unitarity, to all orders in string perturbation theory. We identify regimes in the BFSS matrix model\cite{bfss} and the definition of the S-matrix as the limit of CFT correlators\cite{polchsuss}, which point to the same conclusion. We review a scattering theory based on the quantum mechanics of a finite number of fermionic oscillators, whose algebra formally converges to the Super-Poincare covariant Awada-Gibbons-Shaw\cite{ags} algebra, and argue that a certain class of limiting states on that algebra satisfy all the properties required by physical unitarity in the algebraic formulation of quantum mechanics. The only missing ingredient for a consistent theory is a proof that the S matrix amplitudes themselves are Poincare invariant. We provide suggestive arguments, but no real proof, that this is so.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑