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marcus

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## Main Question or Discussion Point

Increasingly QG is being done with a q-deformed symmetry group: replacing SU(2) by

the quantum group SU

One intuitive justification is that in a universe with a minimum measurable size and an a maximum distance to horizon there is an inherent uncertainty in determining

http://arxiv.org/abs/1105.1898

Eugenio Bianchi, Carlo Rovelli

(Submitted on 10 May 2011)

Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We consider here a different geometrical interpretation of this cut-off, where the relevant non-commutative space is the space of directions around any spacetime point. The limitations in angular resolution expresses the finiteness of the angular size of a Planck-scale minimal surface at a maximum distance [itex]1/\sqrt{\Lambda}[/itex] related the cosmological constant Lambda.

This yields a simple geometrical interpretation for the relation between the quantum deformation parameter

[tex]q=e^{i \Lambda l_{Planck}^2} [/tex]

and the cosmological constant, and resolves a difficulty of more conventional interpretations of the physical geometry described by quantum groups or fuzzy spaces.

Comments: 2 pages, 1 figure

The cosmo constant is a reciprocal area: a handle on it is the distance [itex]1/\sqrt{\Lambda}[/itex] which is easy to calculate by typing this into the google window:

c/(70.4 km/s per Mpc)/sqrt 3/sqrt 0.728

the quantum group SU

_{q}(2). What do you see as the intuitive basis for this?One intuitive justification is that in a universe with a minimum measurable size and an a maximum distance to horizon there is an inherent uncertainty in determining

**angle**. A minimal angular resolution---which SU_{q}(2) nicely implements. The argument is simple and is worked out in this 2-page paper.http://arxiv.org/abs/1105.1898

**A note on the geometrical interpretation of quantum groups and non-commutative spaces in gravity**Eugenio Bianchi, Carlo Rovelli

(Submitted on 10 May 2011)

Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We consider here a different geometrical interpretation of this cut-off, where the relevant non-commutative space is the space of directions around any spacetime point. The limitations in angular resolution expresses the finiteness of the angular size of a Planck-scale minimal surface at a maximum distance [itex]1/\sqrt{\Lambda}[/itex] related the cosmological constant Lambda.

This yields a simple geometrical interpretation for the relation between the quantum deformation parameter

[tex]q=e^{i \Lambda l_{Planck}^2} [/tex]

and the cosmological constant, and resolves a difficulty of more conventional interpretations of the physical geometry described by quantum groups or fuzzy spaces.

Comments: 2 pages, 1 figure

The cosmo constant is a reciprocal area: a handle on it is the distance [itex]1/\sqrt{\Lambda}[/itex] which is easy to calculate by typing this into the google window:

c/(70.4 km/s per Mpc)/sqrt 3/sqrt 0.728

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