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arXiv 1306.4645math-phhep-thmath.MP
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Elko旋量场与大质量类磁单极

Elko Spinor Fields and Massive Magnetic Like Monopoles

E. Capelas de Oliveira, W. A. Rodrigues, J. Vaz

摘要:

本文回顾了λ型和ρ型Elko旋量场通过构造满足一个耦合的一阶偏微分方程组(csfopde),一旦相互作用,就导出λ型和ρ型Elko旋量场的Klein-Gordon方程。由于csfopde是基本的,并且由于λ和ρ的Klein-Gordon方程具有的解不是λ和ρ的csfopde的解,我们推断,将这些场的质量维归为3/2(如狄拉克旋量场的情况)而不是最近文献中所建议的质量维1是合理的(见参考文献列表)。这一事实的一个证明是通过从拉格朗日量导出λ和ρ的csfopde来提供的,其中这些场确实具有3/2的质量维。认真考虑的观点,埃尔科旋量领域由于其特殊性质所给予的双线性不变量可能是某种粒子在现实世界中的描述,然后出现的问题:什么是物理意义的这些领域?在这里,我们提出,场λ和ρ用于构建场K和M的目的(参见等式10)。(38)),它们是表示Clifford丛中的旋量场的Clifford值多形式场。它们是电中性的,不耦合到电磁场,但携带类似磁的电荷,允许它们耦合到su(2)值的电势。如果电势是短程的,那么由K场和M场描述的粒子可能会相互作用,形成类似于暗物质的零自旋粒子凝聚体,因为它们不与电磁场(由带电粒子产生)耦合,因此是不可见的。我们计算了K场和M场的正确传播子。我们还讨论了Elko和Majorana旋量场之间的主要区别。

英文摘要:

In this paper we recall that by construction Elko spinor fields of λ and ρ types satisfy a coupled system of first order partial differential equations (csfopde) that once interacted leads to Klein-Gordon equations for the λ and ρ type fields. Since the csfopde is the basic one and since the Klein-Gordon equations for λ and ρ possess solutions that are not solutions of the csfopde for λ and ρ we infer that it is legitimate to attribute to those fields mass dimension 3/2 (as is the case of Dirac spinor fields) and not mass dimension 1 as previously suggested in recent literature (see list of references). A proof of this fact is offered by deriving the csfopde for the λ and ρ from a Lagrangian where these fields have indeed mass dimension 3/2. Taking seriously the view that Elko spinor fields due to its special properties given by their bilinear invariants may be the description of some kind of particles in the real world a question then arises: what is the physical meaning of these fields? Here we proposed that the fields λ and ρ serve the purpose of building the fields K and M (see Eq.(38))which are Clifford valued multiform fields representing spinor fields in the Clifford bundle. They are electrically neutral and do not couple to the electromagnetic field but carry magnetic like charges which permit them to couple to a su(2) valued potential. If the potential is of short range the particles described by the K and M fields may be interacting and forming condensates of zero spin particles analogous to dark matter, in the sense that they do not couple with the electromagnetic field (generated by charged particles) and are thus invisible. We calculate the correct propagators for the K and M fields. We discuss also the main difference between Elko and Majorana spinor fields.

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