Fermionic zero modes on domain walls
Fermionic zero modes on domain walls
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DOI：
10.1103/physrevd.63.025010
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发表时间：
2000-07
影响因子：
5
通讯作者：
D. Stojkovic
中科院分区：
文献类型：
--
作者：
D. Stojkovic
研究了畴壁背景下的费米子零模。费米子有狄拉克和左右旋马约拉纳质量项。狄拉克质量项的来源是与标量场的耦合。马约拉纳质量项的来源也可能是与标量场$\Phi$的耦合，或者是在远高于场$\Phi$相变的相变中获得的其他场的真空期望值。导出了费米子运动方程，并找到了零模存在的充分必要条件。我们也用数值方法求解。在没有马约拉纳质量项的情况下，方程可以解析解。在无质量费米子的情况下，存在一个零能量解，我们表明，虽然这个模式不是离散归一化的，但它是狄拉克函数归一化的，应该被视为连续谱的一部分，而不是一个孤立的零模式。
We study fermionic zero modes in the domain wall background. The fermions have Dirac and left- and right-handed Majorana mass terms. The source of the Dirac mass term is the coupling to a scalar field $\Phi$. The source of the Majorana mass terms could also be the coupling to a scalar field $\Phi$ or a vacuum expectation value of some other field acquired in a phase transition well above the phase transition of the field $\Phi$. We derive the fermionic equations of motion and find the necessary and sufficient conditions for a zero mode to exist. We also find the solutions numerically. In the absence of the Majorana mass terms, the equations are solvable analytically. In the case of massless fermions a zero energy solution exists and we show that although this mode is not discretely normalizable it is Dirac delta function normalizable and should be viewed as part of a continuum spectrum rather than as an isolated zero mode.