利用zeta函数技术对Yang-Mills-Nahm方程有限能隙解的量子修正
Quantum corrections to finite-gap solutions for Yang-Mills-Nahm equations via zeta-function technique
摘要：
从代数几何的观点考虑一维Yang-Mills-Nahm模型。考虑了一类椭圆型势热方程基于路径积分及其zeta函数对角表示的模型的准经典量子化。格林函数对角线，因此，zeta函数及其导数通过Hermit方程的解表示，或者，通过Its-Matveev形式主义在黎曼teta函数方面。对于Nahm模型，其场通过构造椭圆（双纽线）积分表示，对作用的单圈量子校正被评估为在超椭圆积分方面的零点处的zeta函数导数。替代表达式应有助于连接的表示和继续杨-米尔斯-纳姆模型的调查。关键词：纳姆模型，单圈量子修正，zeta函数，椭圆势，超椭圆积分，Its-Matveev公式。MSC编号：81 Q30、35 J10、35 K 08、81 T13。
英文摘要：
One-dimensional Yang-Mills-Nahm models are considered from algebrogeometric points of view. A quasiclassical quantization of the models based on path integral and its zeta function representation in terms of a Green function diagonal for a heat equation with an elliptic potential is considered. The Green function diagonal and, hence, zeta function and its derivative are expressed via solutions of Hermit equation and, alternatively, by means of Its-Matveev formalism in terms of Riemann teta-functions. For the Nahm model, which field is represented via elliptic (lemniscate) integral by construction, one-loop quantum corrections to action are evaluated as the zeta function derivative in zero point in terms of a hyperelliptic integral. The alternative expression should help to link the representations and continue investigation of the Yang-Mills-Nahm models. Keywords: Nahm model, one-loop quantum corrections, zeta function, elliptic potential, hyperelliptic integral, Its-Matveev formula. MSC numbers: 81Q30, 35J10, 35K08, 81T13.
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