卡塔纳耶夫 - 沃洛维奇模型中的规范未固定哈密顿卡西米尔与静态扭量部分
Gauge-Unfixed Hamiltonian Casimir and Static Torsionful Sector in the Katanaev-Volovich Model
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中文总结 AI 辅助
研究二维引力的一阶卡塔纳耶夫 - 沃洛维奇模型，通过哈密顿分析等方法，恢复卡塔纳耶夫/泊松 - 西格玛卡西米尔，确定其为约化正则部分的全局标签，还发现挠率对相关物理量有影响，卡西米尔归一化的第一定律成立。
中文摘要 AI 辅助
对具有挠率的二维引力的一阶卡塔纳耶夫 - 沃洛维奇模型进行哈密顿分析。一阶作用量已挑选出自然的正则对：辅助洛伦兹标量与空间联络和 zweibein 共轭。扩展的狄拉克 - 伯格曼嵌入分离出一个辅助的二类部分，消除该部分可恢复一阶作用量中编码的正则结构，并留下产生局部规范对称性的一类约束。独立的法捷耶夫 - 雅基夫约化产生相同的约化括号。然后在施加任何规范条件之前，直接从约化的狄拉克 - 伯格曼一类约束理想中恢复卡塔纳耶夫/泊松 - 西格玛卡西米尔，直至归一化。这将卡西米尔识别为约化正则部分的全局标签；选择静态归一化后，它提供扭量分支的哈密顿参数。在伸缩子规范中对该分支应用相同的归一化，其场方程在壳上得到验证。在这个静态部分，卡西米尔归一化的径向场与度规克利福德范数不一致：对角代表满足\(NB = e^{4\beta r}\)。因此，挠率通过克利福德时间的归一化修改了克利福德温度，而视界熵保持其标准的二维伸缩子值，并且卡西米尔归一化的第一定律成立。
英文摘要
Hamiltonian analysis of the first-order Katanaev-Volovich model of two-dimensional gravity with torsion. The first-order action already singles out natural canonical pairs: the auxiliary Lorentz scalars are conjugate to the spatial connection and zweibein. An extended Dirac-Bergmann embedding isolates an auxiliary second-class sector whose elimination recovers the canonical structure encoded in the first-order action and leaves the first-class constraints generating the local gauge symmetries. An independent Faddeev-Jackiw reduction yields the same reduced brackets. The Katanaev/Poisson-Sigma Casimir is then recovered, up to normalization, directly from the reduced Dirac-Bergmann first-class constraint ideal, before imposing any gauge condition. This identifies the Casimir as a global label of the reduced canonical sectors; after the static normalization is chosen, it supplies the Hamiltonian parameter of the torsionful branch. The same normalization is applied to that branch in dilaton gauge, whose field equations are verified on shell. In this static sector the Casimir-normalized radial field does not coincide with the metric Killing norm: the diagonal representative satisfies \(NB=e^{4βr}\). Consequently, torsion modifies the Killing temperature through the normalization of the Killing time, while the horizon entropy retains its standard two-dimensional dilaton value and the Casimir-normalized first law holds.
