A. Zee, Quantum Field Theory in a Nutshell · Problem VIII.1.4

Field Theory Redux

Physics — QFT

Problem

Count the number of degrees of polarization of a graviton. [Hint: Consider a plane wave

h_{\mu\nu}(k)e^{ikx}

just because it is a bit easier to work in momentum space. A symmetric tensor has 10 components and the harmonic gauge

k_\mu h^\mu{}_\nu = \frac{1}{2}k_\nu h^\lambda{}_\lambda

imposes 4 conditions. Oops, we are left with 6 degrees of freedom. What is going on?] [Hint: You can make a further gauge transformation and still stay in the harmonic gauge. The graviton should have only 2 degrees of polarization.]

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