Back in 2003 we here at PF studied papers by Sahlmann and by Lewandowski/Okolow about a basic algebra of LQG called the(adsbygoogle = window.adsbygoogle || []).push({});

"holonomy-flux algebra".

It is a star-algebra and anyone familiar with its construction will realize that it is NOT generally the case that a = a* for some element a in [tex]\frak{A}[/tex].

Pretending that a = a* for all stuff in the holonomy-flux algebra is kind of like supposing that all complex numbers are real----that is, saying that each z is equal to its own conjugate.

If you assume something that wrong then you can prove or disprove pretty much anything you want as a logical consequence. Like, if 1 = 2 then Moonbear is the Queen of France, or whatever. QED.

But although we studied [tex]\frak{A}[/tex] quite a bit back in 2003, people forget and it is probably time for a refresher (I am sure I would benefit from a review). And it is especially appropriate because a long-awaited paper by Lewandowski-et-al just came out.

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# Holo-flux alg aint all a=a*

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