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arXiv math-ph/0701076math-phmath.MPmath.OA
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再论行列式的乘法反常;定域性

The multiplicative anomaly for determinants revisited; locality

Marie-Francoise Ouedraogo, Sylvie Paycha

摘要:

观察到两个椭圆算子的乘积的对数不同于由算子括号的有限和的乘积的总和,我们推断,这种差异的正则化的痕迹是本地的非交换剩余的有限和。从一个明确的本地公式,这样正规化的痕迹,我们推导出一个明确的本地公式的乘法异常的ζ-决定因素,揭示了它的地方,并产生以前已知的结果。

英文摘要:

Observing that the logarithm of a product of two elliptic operators differs from the sum of the logarithms by a finite sum of operator brackets, we infer that regularised traces of this difference are local as finite sums of noncommutative residues. From an explicit local formula for such regularised traces, we derive an explicit local formula for the multiplicative anomaly of zeta-determinants which sheds light on its locality and yields back previously known results.

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。

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