Canepa G, Cattaneo A S, Schiavina M
Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zurich, Switzerland.
Institute for Theoretical Physics, ETH Zurich, Wolfgang Pauli strasse 27, 8092 Zurich, Switzerland.
Commun Math Phys. 2021;385(3):1571-1614. doi: 10.1007/s00220-021-04127-6. Epub 2021 Jul 2.
In this note the AKSZ construction is applied to the BFV description of the reduced phase space of the Einstein-Hilbert and of the Palatini-Cartan theories in every space-time dimension greater than two. In the former case one obtains a BV theory for the first-order formulation of Einstein-Hilbert theory, in the latter a BV theory for Palatini-Cartan theory with a partial implementation of the torsion-free condition already on the space of fields. All theories described here are BV versions of the same classical system on cylinders. The AKSZ implementations we present have the advantage of yielding a compatible BV-BFV description, which is the required starting point for a quantization in presence of a boundary.
在本笔记中，AKSZ构造被应用于在大于二维的每个时空维度下爱因斯坦 - 希尔伯特理论和帕拉蒂尼 - 嘉当理论约化相空间的BFV描述。在前一种情况下，得到了爱因斯坦 - 希尔伯特理论一阶表述的BV理论，在后一种情况下，得到了帕拉蒂尼 - 嘉当理论的BV理论，且在场空间上已经部分实现了无挠条件。这里描述的所有理论都是圆柱上同一经典系统的BV版本。我们给出的AKSZ实现具有产生兼容的BV - BFV描述的优点，这是存在边界时进行量子化所需的起点。
