论文标题
减少了$ u（1）^3 $模型的相位空间方法的欧几里得量子重力
Reduced Phase Space Approach to the $U(1)^3$ model for Euclidean Quantum Gravity
论文作者
论文摘要
如果通过其$ u（1）^3 $版本代替了Ashtekar-Barbero $ su（2）$量规理论的限制，欧几里得重力的公式，则可以捕获其$ SU（2）$版本的重要结构一致的模型。特别是，它显示出非尖端变形代数的非微不足道实现，这使其成为（Euclidean）量子重力的有趣测试场，正如Varadarajan等人最近的一系列论文中所强调的那样。在本文中，我们考虑了该模型的相位空间方法减少。这是特别有吸引力的，因为在经典的转换之后，最大的约束是在动矩中的{\ it线性}。因此，在合适的仪表中，可以找到一个仅取决于物理观察物的物理哈密顿量的封闭式和明确的公式。毫不奇怪，该物理哈密顿量通常既不是多项式也不是局部的。由于Varadarajan等人，相应的减少相位空间定量可以面对约束定量，以进一步了解超出表面变形代数的量子实现。
If one replaces the constraints of the Ashtekar-Barbero $SU(2)$ gauge theory formulation of Euclidean gravity by their $U(1)^3$ version, one arrives at a consistent model which captures significant structure of its $SU(2)$ version. In particular, it displays a non trivial realisation of the hypersurface deformation algebra which makes it an interesting testing ground for (Euclidean) quantum gravity as has been emphasised in a recent series of papers due to Varadarajan et al. In this paper we consider a reduced phase space approach to this model. This is especially attractive because, after a canonical transformation, the constraints are at most {\it linear} in the momenta. In suitable gauges, it is therefore possible to find a closed and explicit formula for the physical Hamiltonian which depends only on the physical observables. Not surprisingly, that physical Hamiltonian is generically neither polynomial nor spatially local. The corresponding reduced phase space quantisation can be confronted with the constraint quantisation due to Varadarajan et al to gain further insights into the quantum realisation of the hypersurface deformation algebra.
