Holonomy Operator and Quantization Ambiguities on Spinor Space
Holonomy Operator and Quantization Ambiguities on Spinor Space
复制标题
旋量空间上的完整算子和量化模糊度
DOI：
10.1103/physrevd.87.104014
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发表时间：
2013
影响因子：
5
通讯作者：
J. Tambornino
中科院分区：
文献类型：
--
作者：
E. Livine;J. Tambornino
我们在最近开发的环引力旋量公式中构造了完整通量算子代数。我们证明，当限制于 SU(2) 规范不变算子时，熟悉的抓取和 Wilson 循环算子被编写为复合算子，这些算子是根据最近在 $\mathrm{U}(N)$ 交织器和自旋网络方法中引入的规范不变“广义梯形算子”构建的。我们对完整算子定义中出现的量化模糊性进行评论，并使用这些模糊性作为玩具模型来测试圈量子引力中哈密顿约束算子的标准正则化和定义中存在的一类量化模糊性。
We construct the holonomy-flux operator algebra in the recently developed spinor formulation of loop gravity. We show that, when restricting to SU(2)-gauge invariant operators, the familiar grasping and Wilson loop operators are written as composite operators built from the gauge-invariant ``generalized ladder operators'' recently introduced in the $\mathrm{U}(N)$ approach to intertwiners and spin networks. We comment on quantization ambiguities that appear in the definition of the holonomy operator and use these ambiguities as a toy model to test a class of quantization ambiguities which is present in the standard regularization and definition of the Hamiltonian constraint operator in loop quantum gravity.