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arXiv 0907.1530gr-qc
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来自外部标量场的Immirzi参数

The Immirzi parameter from an external scalar field

Francesco Cianfrani, Giovanni Montani

摘要:

将Immirzi参数推广为最小耦合标量场,在无时间规范的圈量子引力框架下分析了哈密顿约束.正确的SU(2)联络可以被定义,并且包含域$β$的导数的项进入它们的定义。此外,助推自由度是非动力学的,而超动量约束符合标量场的情况。因此,运动学希尔伯特空间可以定义为存在最小耦合标量场的引力空间。然后,我们分析了这种情况下的动力学含义,我们概述了如何预测一个非零真空期望值的动力学弛豫。

英文摘要:

We promote the Immirzi parameter to be a minimally coupled scalar field and we analyzed the Hamiltonian constraints in the framework of Loop Quantum Gravity without the time gauge. Proper SU(2) connections can be defined and a term containing derivatives of the field $β$ enters into their definition. Furthermore, boost degrees of freedom are non-dynamical, while the super-momentum constraints coincide with the scalar field case. Hence, the kinematical Hilbert space can be defined as for gravity in presence of a minimally coupled scalar field. Then, we analyzed the dynamical implications of this scenario and we outlined how a the dynamical relaxation to a non-vanishing vacuum expectation value is predicted.

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