Glen Ropella asked: >What is that ^ symbol between dx^a and dx^b? Roger Critchlow writes: > Working from the context, I'd guess: the tensor >product between the components <i>dx<sup>a</sup></i> >and <i>dx<sup>b</sup></i>of the stress energy tensor > <i>T<sub>ab</sub></i>, but I've never been too sure ' >about tensors.
I haven't read the Verlinde paper (and don't intend to; I find that treating string theoretical physicists as ignorable crackpots who, alas, have immense institutional power makes my life much simpler), but my guess about the "^" symbol is that it's meant to be the "wedge product" or "exterior product" rather than the general tensor product--in other words, it's skew-symmetric. As an example, in old fashioned terms, the tensor product of two vectors in R3, a = a1x1+a2x2+a3x3 and b = b1x1+b2x2+b3x3, where you can make the indices of ai and bj be lower and those on x be upper if you like, is the "dyad" ab = a1b1x1x1+a1b2x1x2+...+a3b3x3x3, which skew-symmetrizes to a^b = (a1b2-a2b1)x1^x2 + (a1b3-a3b1)x1^x3 + (a2b3-a3b2)x2^x3 (or maybe, depending on taste, to that divided by 2 or 3 factorial). ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
