Theoretical possibilities of models of gravity with dynamical signature are discussed. The different scenarios of the signature change are proposed in the framework of Einstein-Cartan gravity. We consider, subsequently, the dynamical signature in the model of the complex manifold with complex coordinates and complex metrics are introduced, a complexification of the manifold and coordinates through new gauge fields, an additional gauge symmetry for the Einstein-Cartan vierbein fields, and non-flat tangent space for the metric in the Einstein-Cartan gravity. A new small parameter, which characterizes a degree of the deviation of the signature from the background one, is introduced in all models. The zero value of this parameter corresponds to the signature of an initial background metric. In turn, in the models with gauge fields present, this parameter represents a coupling constant of the gauge symmetry group. The mechanism of metric determination through induced gauge fields with defined signatures in the corresponding models is considered. The ways of the signature change through the gauge field dynamics are reviewed, and the consequences and applications of the proposed ideas are discussed as well.

中文翻译：

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动态特征：复杂流形、规范场和非平面切线空间

讨论了具有动态特征的重力模型的理论可能性。在爱因斯坦-嘉当引力的框架下提出了签名变化的不同场景。随后，我们考虑了具有复坐标和复度量的复流形模型中的动态特征，通过新规范场对流形和坐标进行复化，爱因斯坦-嘉当维尔宾场的附加规范对称性，以及非-爱因斯坦-嘉当引力中度量的平面切线空间。在所有模型中都引入了一个新的小参数，该参数表征了签名与背景的偏差程度。此参数的零值对应于初始背景度量的签名。反过来，在存在规范场的模型中，该参数表示规范对称群的耦合常数。考虑了通过在相应模型中定义签名的诱导规范场来确定度量的机制。回顾了通过规范场动力学改变特征的方式，并讨论了所提出的想法的后果和应用。