Recent content by albedo

If the google books links does not work, you can also see at p. 70 and the paragraph just before the eq. 3.7 of the DRAFT version of the book...

Please refer to p. 99 and 100 of Rovelli’s Quantum Gravity book (here). I wonder what is the signification of the “naturalness” of the definition of ##\theta_0=p_idq^i##? If I take ##\theta_0'=q^idp_i## inverting the roles of the canonical variables and have the symplectic 2-forms of the...

I think Haelfix's last post goes well along with the text from Thomas Thiemann, HERE, which probably grounds the argument more technically. As long as you change only ##M## under a coordinate transformation (passive diffeomorphism), the spatial volume ##V_R(q)## does change. However, if you...

Oh yes, thank you. The two notations in the definition tell exactly the same :smile:

I stand with you with the demonstration but I think you should use the definition of the Lie derivative by including the flow map instead of p in the first term of the numerator (and similarly in the following lines): ##(\mathcal L_XY)_p =\lim_{t\to 0}\frac{((\phi_{-t})_*Y)_...

Wonderful, Fredrik, I will go through this great exercise when a bit of time. In the meantime (and should this take not much of your time !) can you comment on (i) how intuitively you would explain the -t appearing in ##\phi_{-t}## in your definition; what does it means physically? and (ii) the...

Thank you. Maybe a bit off topic but how I can recover from your definition the abstract definition as the Lie bracket or commutator of vector fields? ##(\mathcal L_XY)_p=[X,Y]_p##. Am I wrong in the abstract definition?

Yes, you are right. If that was not the case, then the general covariance (or active diffeomorphism invariance or background independence) would have been broken and I would end up with an a priori structure defined by that particular field.

Thank you attyy and stevendaryl for your clarifications. I think stevendaryl has nailed it down well. Adding an extra step to the argumentation, I think it is precisely realizing that you can always find a transformation such that \mathcal{C}(\tilde{g})_{\mu \nu} = \tilde{\mathcal{C}}(g)_{\mu...

Yes, it must be so. Thank you for the link to Luca Lusanna’s paper and his explication of that duality: “…Let us recall that there is another, non-geometrical - so-called dual – way of looking at the active diffeomorphisms, which, incidentally, is more or less the way in which Einstein himself...

Just wish to add that the p. 63 and p. 64 of Rovelli's book are given on-line HERE.

I am new here but tried to go through some of the posts on subject matter: I apologize if I am overlooking your input as I am sure you must have clarified already my naive doubts ! I just completed a first reading of Carlo Rovelli's Quantum Gravity book (hardcover edition, 2004). I find the...