SU(2) and SU(1,1) Y-Maps in Loop Quantum Gravity
Tóm tắt
In this paper we first provide the proof of
$$\hbox {SU}(2)$$
Y-Map convergence. Then, by using
$$\hbox {SU}(1,1)$$
LQG simplicity constraints, we define
$$\hbox {SU}(1,1)$$
Y-Map from infinitely differentiable with a compact support functions on
$$\hbox {SU}(1,1)$$
to the functions (not necessarily square integrable) on
$$\hbox {SL}(2,C)$$
, and prove its convergence as well.
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