标题： 实洛伦兹广义相对论的自旋联络表述 显示英文标题

标题： Spin connection formulations of real Lorentzian General Relativity

摘要： 我们推导了实四维洛伦兹真空广义相对论的纯旋量联络和无约束的BF形式化方法。与现有的复形式化相比，一个重要优势是它们不需要使量子化复杂化的现实性约束。我们还考虑了相应的修正引力理论，并指出，与自对偶类比理论不同，这些理论不可行，因为它们必然包含鬼场。特别是，这限制了可以通过扩展规范群来构建的潜在可行统一理论的集合，使其具有广义相对论的作用结构。然而，我们发现所得出的理论不承认经典解。这一问题可以通过引入额外的动力学场来解决，顺便说一下，这也可能提供了一种包含物质领域的方式。 显示英文摘要

摘要： We derive the pure spin connection and constraint-free BF formulations of real four-dimensional Lorentzian vacuum General Relativity. In contrast to the existing complex formulations, an important advantage is that they do not require the reality constraints that complicate quantization. We also consider the corresponding modified gravity theories and point out that, contrary to their self-dual analogues, they are not viable because they necessarily contain ghosts. In particular, this constrains the set of potentially viable unified theories one can build by extending the gauge group to the ones with the action structure of General Relativity. We find, however, that the resulting theories do not admit classical solutions. This issue can be solved by introducing extra dynamical fields which, incidentally, could also provide a way to include a matter sector.