I know that the polarisation vector is not lorentz invariant. But how exactly can I derive the lorentz boosted polarisation vector for a spin-1 particle (say photon)?
What about spin-2 particle's polarisation?
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$\begingroup$ The polarisation vector has a little group (Wigner) index and a Lorentz index. It transforms as a tensor product, $u^A_s(p)\to L(\Lambda)^A{}_B D(W)_s{}^{s'}u^B_{s'}(\Lambda)$, with $L$ the representation of Lorentz and $D$ the representation of the orthogonal group (with $W$ the Wigner matrix associated to $\Lambda$). This is standard textbook material (see e.g. Weinberg's QFT, Vol I). $\endgroup$– AccidentalFourierTransformCommented Apr 6, 2018 at 16:11
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$\begingroup$ related: What are the actual transformation properties of Dirac spinors $u_\sigma(p)$?. $\endgroup$– AccidentalFourierTransformCommented Apr 6, 2018 at 16:13
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1 Answer
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The polarization properties of masselss particles with any spin (and hence in particular for spin 2) are discussed in detail in Weinberg's papers
S. Weinberg, Feynman rules for any spin II. Massless particles, Phys. Rev. 134 (1964), B882--B896.
S. Weinberg, Feynman rules for any spin III, Phys. Rev. 181 (1969), 1893--1899.
Everything is roughly analogous to the well-known spin 1 case.
answered Apr 13, 2018 at 10:08