Canonical quantization of Ashtekar's new variables

[kodama]

TL;DR Summary

correct ?

This year I’m hoping to integrate ideas about “quantization” into the course more than in the past, starting off with the mathematics behind what physicists often call “canonical quantization”. This topic is worked out very explicitly and in great detail in this book-
Spring Course
Posted on January 10, 2023 by woit

Is Loop quantum gravity canonical quantization of Ashtekar's new variables
correct ?

if not in principle is there any particular ways to canonical quantization of Ashtekar's new variables ?

are there other methods to quantization of Ashtekar's new variables ?

 

[Demystifier]

Loop quantum gravity is not exactly a quantization of Ashtekar variables. Instead, Ashtekar variables are an important step towards construction of variables that are quantized in loop quantum gravity. As far as I know, there is no direct quantization of Ashtekar variables. And finally, those variables are no longer "new".

 

[kodama]

Loop quantum gravity is not exactly a quantization of Ashtekar variables. Instead, Ashtekar variables are an important step towards construction of variables that are quantized in loop quantum gravity. As far as I know, there is no direct quantization of Ashtekar variables. And finally, those variables are no longer "new".

is quantization of Ashtekar variables possible and would be a

quantum gravity