- #1

tom.stoer

Science Advisor

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## Main Question or Discussion Point

I am a new member; I hope I didn't miss existing questions and answers.

One of my questions regarding loop quantum gravity / Ashtekar variables is: what is the relation between the familiar SO(3,1) Lorentz symmetry of special relativity and the local SU(2) symmetry of the vierbein-rotation introduced in Ashtekar's formulation. Are they more or less identical in the sense as SO(3,1) ~ SU(2)*SU(2) ? Or is it not allowed to think of the gauge symmetry in Ashtekar's formulation as Lorentz symmetry?

If this local symmetry is related to the Lorentz symmetry: why only Lorentz and not Poincare?

Thanks

Thomas

One of my questions regarding loop quantum gravity / Ashtekar variables is: what is the relation between the familiar SO(3,1) Lorentz symmetry of special relativity and the local SU(2) symmetry of the vierbein-rotation introduced in Ashtekar's formulation. Are they more or less identical in the sense as SO(3,1) ~ SU(2)*SU(2) ? Or is it not allowed to think of the gauge symmetry in Ashtekar's formulation as Lorentz symmetry?

If this local symmetry is related to the Lorentz symmetry: why only Lorentz and not Poincare?

Thanks

Thomas