Spin-1 massless particles are transverse waves, so they need at least three space-time dimensions to exists. As for gravitons, I think they are still not possible in three dimensions, and to reveal their true nature one needs at least four dimensions; otherwise there would be no way to distinguish a graviton form a vector in such a three dimensional universe. Other argument against it is the fact that there's only (grav.) radiation in four or more dimensions, but I'm looking for a "theorem" more in the context of field theory.
Asked
Active
Viewed 173 times
1
Qmechanic
- 201,751
-
Possible duplicates: https://physics.stackexchange.com/q/68824/2451 , https://physics.stackexchange.com/q/74307/2451 and links therein. – Qmechanic Feb 03 '21 at 20:22
-
If the perturbative field doesn't have any degrees of freedom not determined by $T_{ab}$, as is the case for 2+1 gravity (the Weyl tensor vanishes), what are you even quantizing? – Zo the Relativist Feb 03 '21 at 20:30
-
Is your question essentially if it is (im)possible to write down a theory for a dynamical massless spin-2 field in 2+1 dimensions? – TimRias Feb 03 '21 at 20:31
-
I don't follow your reasoning for e.g. electromagnetism in 2 dimensions. But indeed for gravity you have no dofs in 3 dimensions: massless gravity is famously topological (https://inspirehep.net/literature/21208) but not for the reason you mention. – Feb 03 '21 at 21:55