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arXiv 0704.0553hep-thhep-ph
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自发洛伦兹破坏：非阿贝尔规范场的赝Goldstone矢量玻色子

Spontaneous Lorentz Violation: Non-Abelian Gauge Fields as Pseudo-Goldstone Vector Bosons

J. L. Chkareuli, J. G. Jejelava

备注：
Invited talk given at Caucasian-German School and Workshop in Hadron Physics (4-7 September 2006, Tbilisi, Georgia)
发表信息：
Phys.Lett.B659:754-760,2008
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摘要：

我们认为，非阿贝尔规范场可以看作是由自发洛伦兹不变性破坏（SLIV）引起的赝戈德斯通矢量玻色子。为此，SLIV演变的一般杨米尔斯型理论与非线性矢量场约束$Tr(% \boldsymbol{A}_{μ}\boldsymbol{A}^μ)=\pm M^{2}$（$M$是一个建议SLIV规模）施加被详细考虑。由于内部对称群$G$具有$D$生成元，不仅纯洛伦兹对称SO（1，3），而且SLIV约束本身的更大的偶然对称$SO(D,3D)$似乎也自发破缺。因此，虽然纯洛伦兹破坏仍然只产生一个真正的戈德斯通矢量玻色子，但伴随的与$SO(D,3D)$破缺有关的伪戈德斯通矢量玻色子也在整个戈德斯通矢量场多重态的最终排列中发挥作用。值得注意的是，它们仍然是严格无质量的，受到杨-米尔斯理论的规范不变性的保护。我们发现，虽然这个理论包含了大量的洛伦兹和$CPT$违反耦合，他们不会导致物理SLIV效果，原来被严格取消在所有的最低阶过程考虑。然而，如果内部规范不变性在受引力影响的非常小的距离上被轻微破坏，物理洛伦兹破坏就可能出现。对于与普朗克尺度相当的SLIV尺度，洛伦兹破坏可以在低能量下直接观察到。

英文摘要：

We argue that non-Abelian gauge fields can be treated as the pseudo-Goldstone vector bosons caused by spontaneous Lorentz invariance violation (SLIV). To this end, the SLIV which evolves in a general Yang-Mills type theory with the nonlinear vector field constraint $Tr(% \boldsymbol{A}_{μ}\boldsymbol{A}^μ)=\pm M^{2}$ ($M$ is a proposed SLIV scale) imposed is considered in detail. With an internal symmetry group $G$ having $D$ generators not only the pure Lorentz symmetry SO(1,3), but the larger accidental symmetry $SO(D,3D)$ of the SLIV constraint in itself appears to be spontaneously broken as well. As a result, while the pure Lorentz violation still generates only one genuine Goldstone vector boson, the accompanying pseudo-Goldstone vector bosons related to the $SO(D,3D)$ breaking also come into play in the final arrangement of the entire Goldstone vector field multiplet. Remarkably, they remain strictly massless, being protected by gauge invariance of the Yang-Mills theory involved. We show that, although this theory contains a plethora of Lorentz and $CPT$ violating couplings, they do not lead to physical SLIV effects which turn out to be strictly cancelled in all the lowest order processes considered. However, the physical Lorentz violation could appear if the internal gauge invariance were slightly broken at very small distances influenced by gravity. For the SLIV scale comparable with the Planck one the Lorentz violation could become directly observable at low energies.

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