View Full Version : Question about graviton polarization tensor

Alessandro Andres
2009-Jun-20, 12:37 PM
Hi Iím a student, and I started reading Zwiebachís First Course in String Theory, but I still havenít learned general relativity, only special relativity, and so Iím having some difficulties in understanding the polarization tensor for the perturbation of the Minkowski metric leading to the graviton. I understand the transverse traceless and symmetry condition, but I got stuck in an issue: shouldnít a positivity condition be assumed for the off-diagonal symmetric components of the polarization tensor? What does it mean negative off-diagonal components?

Could someone help me with this?


2009-Jun-20, 06:37 PM
Not to sound pedantic, but how about first studying GR before you start on string theory.

Alessandro Andres
2009-Jun-20, 07:09 PM
Thanks, someone also suggested the same.

2009-Jun-21, 11:54 PM
Zweibach's book is written for undergrads, so doesn't assume much of a knowledge of GR. However, if you want to understand all the details, that's helpful. A good GR book on an intro level is Schutz' "A first course in general relativity" book.

I don't believe the polarization tensor needs a positivity condition. I don't see any reason for it offhand. His e.q. 10.110 (in the 1st edition, dont know if the numbering is the same in the second) has the one graviton states in terms of this tensor, and it doesn't look like changing the overall sign would cause a problem here, and I don't see any other problems offhand with changing signs of components. Though I haven't spelled it out carefully.

Schutz' book (and every other GR book) have a discussion of classical gravitational radiation which should discuss this in the classical case. And classically there's no positivity condition, and I don't see a reason offhand to add one quantum mechanically.