发表机构
Constructor University Bremen（不莱梅构造大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究基于分次泊松几何构建场论框架，明确了爱因斯坦-嘉当引力与受约束标架形式的帕拉蒂尼-嘉当引力的等价性，还展示了如何通过分次流形微分同胚关联理论、移除约束得到完整帕拉蒂尼-嘉当理论，并可纳入极小BV扩展。
AI 中文摘要
我们运用分次泊松几何的相关概念，构建了一个可对爱因斯坦-嘉当引力、帕拉蒂尼-嘉当引力等场论进行简洁表述的框架。研究表明，爱因斯坦-嘉当引力等价于帕拉蒂尼-嘉当引力的一种变体，该变体中标架场需满足恰当的对称关系，我们将其称为受约束标架引力。为此，我们通过分次流形的微分同胚建立了这些理论间的关联。随后，我们展示了如何通过移除对称约束得到完整的帕拉蒂尼-嘉当理论。最后，我们证明了该分次几何框架可直接将受约束标架引力与帕拉蒂尼-嘉当引力的极小BV扩展纳入其中。
英文摘要
Using notions from graded Poisson geometry, we develop a framework that allows for concise formulations of field theories such as Einstein-Cartan and Palatini-Cartan gravity. We show that Einstein-Cartan gravity is equivalent to a variant of Palatini-Cartan gravity in which the vielbein fields are constrained to satisfy appropriate symmetry relations, which we refer to as constrained vielbein gravity. To that end, we relate these theories via a diffeomorphism of graded manifolds. We then show how to obtain the full Palatini-Cartan theory by removing the symmetry constraint. Finally, we show how our graded geometric framework allows for a direct incorporation of the minimal BV extension of the graded constrained vielbein and Palatini-Cartan theories.
Comments29 pages
