My advisor and I have stumbled upon a very strange claim in Rovelli's book. There he defines the P_diff map from S0 onto its algebraic dual S0* as(adsbygoogle = window.adsbygoogle || []).push({});

P_diff(Psi) Psi' = sum (Psi'' = phi Psi) (Psi'',Psi')

This is indeed a well-defined map that yields diff-invariant states. However, Rovelli claims, further, that the image of this map is indeed the space of _all_ diff-invariant states -- that is, that all diff-invariant states are of the form P_diff(Psi) for some Psi that is a _finite_ sum of spin network states.

However, as I see it, a diff-invariant state f can be seen as an arbitrary mapping of each s-knot state (diffeomorphism equivalence class of spin network states) k to a certain number f(k), whereas if f is of the form P_diff(Psi), with Psi = sum_s Psi_s, then f(k) can only be non-zero for those k which have the same knot as one of these s. Indeed, a simple example such as the state f(k) = 1 for all k is clearly _not_ of the form P_diff Psi. Is this reasoning correct? If so, what is it that one can state about the space K_diff?

Thanks in advance,

-- Rafael Kaufmann

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# The space of diff-invariant states

Loading...

Similar Threads for space diff invariant | Date |
---|---|

A Space is "Entangled", says Leonard Susskind | Sep 13, 2017 |

I Geometry of GR v. Spin-2 Massless Graviton Interpretation | Sep 13, 2017 |

I Kaluza–Klein metric, space between charged capacitor? | Jun 17, 2017 |

A Double field theory: Where is the extra space? | Jun 8, 2017 |

QG five principles: superpos. locality diff-inv. cross-sym. Lorentz-inv. | Aug 7, 2010 |

**Physics Forums - The Fusion of Science and Community**