双向QED
Bimetric QED
摘要：
我们研究，作为一个模型的洛伦兹对称性破缺，量子电动力学的扩展在一个平坦的时空中的光子和电子传播不同，不共享相同的光锥的量子化和重整化。我们将把这个模型称为双度量QED（BIMQED）。作为一个初步的，我们讨论了制定电动力学的预度量形式主义，然而，有一个简单的criteron的基础上，一个首选的度量。从这种度量的选择产生的是Weyl类张量（WLT）。WLT的彼得罗夫分类产生了相应的洛伦兹对称破缺分类。我们不施加任何约束的对称性破缺的强度，并能够获得明确的色散关系的光子在每个彼得罗夫类的传播。相关的双折射在某些情况下表现为两个不同的偏振依赖光锥，在其他情况下表现为一个更复杂的结构，不能以简单的方式解开。我们展示了如何在BIMQED的重整化过程中，除了其对标准参数，如电荷和质量的影响，迫使重整化的指标和WLT。两个特别容易处理的情况下，我们可以得到重整化群流的模型的参数与分析的不动点结构的详细研究。当然，这些结果与以前的研究是一致的，但我们并不局限于处理洛伦兹对称性破缺必然弱。正如我们在以前的研究中发现的标量场理论模型的一个可接受的因果结构的模型施加约束的各种光锥之间的关系BIMQED。
英文摘要：
We study, as a model of Lorentz symmetry breaking, the quantisation and renormalisation of an extension of QED in a flat spacetime where the photons and electrons propagate differently and do not share the same lightcone. We will refer to this model as Bimetric QED (BIMQED). As a preliminary we discuss the formulation of electrodynamics in a pre-metric formalism showing nevertheless that there is, on the basis of a simple criteron, a preferred metric. Arising from this choice of metric is a Weyl-like tensor (WLT). The Petrov classification of the WLT gives rise to a corresponding classification of Lorentz symmetry breaking. We do not impose any constraint on the strength of the symmetry breaking and are able to obtain explicit dispersion relations for photon propagation in each of the Petrov classes. The associated birefringence appears in some cases as two distinct polarisation dependent lightcones and in other cases as a a more complicated structure that cannot be disentangled in a simple way. We show how in BIMQED the renormalisation procedure can, in addition to its effect on standard parameters such as charge and mass, force the renormalisation of the metrics and the WLT. Two particularly tractable cases are studied in detail for which we can obtain renormalisation group flows for the parameters of the model together with an analysis of fixed point structure. Of course these results are consistent with previous studies but we are not constrained to treat Lorentz symmetry breaking as necessarily weak. As we found in a previous study of a scalar field theory model an acceptable causal structure for the model imposes constraints on relationship between the various lightcones in BIMQED.
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。
