电弱瞬子背景下的费米子能级交叉
On the Fermion Level Crossing in the Electroweak Instanton Background
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中文总结 AI 辅助
该研究考虑费米子能量的欧几里得时间依赖性，修改标准费米子近似，证明费米子能谱流动持续时间对应瞬子陈-西蒙斯数1个单位变化，为瞬子背景下的指标定理提供数值验证。
中文摘要 AI 辅助
我们研究电弱瞬子背景下的费米子能级交叉，在从场方程到费米子能级谱流的整个分析中，考虑费米子能量的欧几里得时间依赖性。通过修改标准费米子近似，我们证明，无论模型参数如何，费米子能谱从一个连续区流向另一个连续区的持续时间，对应瞬子的陈-西蒙斯数恰好发生1个单位的变化。我们进一步表明，纳入这种时间依赖性对于建立费米子零模数量与瞬子绕数之间的一一对应关系至关重要，为瞬子背景下的指标定理提供了数值验证。
英文摘要
We investigate fermion level crossing in the electroweak instanton background, taking into account the Euclidean-time dependence of the fermion energy throughout our analysis, from the field equations to the spectral flow of fermion energy levels. Modifying the standard fermion ansatzes, we show that, irrespective of the model parameters, the duration over which the fermion energy spectrum flows from one continuum to another corresponds to exactly one unit change in the Chern--Simons number of the instanton. We further demonstrate that incorporating this time dependence is essential for establishing a one-to-one correspondence between the number of fermion zero modes and the instanton winding number, providing a numerical confirmation of the index theorem in the context of instanton backgrounds.
