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arXiv 1507.01018hep-ph
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奇异Lorentz破坏拉格朗日量及其Finsler结构

Singular Lorentz-Violating Lagrangians and Associated Finsler Structures

Don Colladay, Patrick McDonald

摘要:

在标准模型扩展(SME)中,与洛伦兹破坏费米子的经典极限相关的几个拉格朗日量已经被证明在欧几里得空间中表达理论时产生芬斯勒函数。当自旋耦合存在时,拉格朗日量可以发展出奇点,这阻碍了全局定义的勒让德变换的构建,导致奇异的芬斯勒空间。对出现这种问题的中小企业的一个具体部门进行了研究。结果发现,奇异行为可以消除一个适当的提升的问题相关联的代数簇。这为奇异问题提供了一个光滑的经典模型。在欧几里得空间中,该过程涉及将两个相关的奇异芬斯勒函数组合成单个光滑函数,该函数具有定义在去奇异化簇上的半正定二次型。

英文摘要:

Several lagrangians associated to classical limits of lorenz-violating fermions in the Standard Model extension (SME) have been shown to yield Finsler functions when the theory is expressed in Euclidean space. When spin-couplings are present, the lagrangian can develop singularities that obstruct the construction of a globally defined Legendre transformation, leading to singular Finsler spaces. A specific sector of the SME where such problems arise is studied. It is found that the singular behavior can be eliminated by an appropriate lifting of the problem to an associated algebraic variety. This provides a smooth classical model for the singular problem. In Euclidean space, the procedure involves combining two related singular Finsler functions into a single smooth function with a semi-positive definite quadratic form defined on a desingularized variety.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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