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Unformatted text preview: Physics 509: Relativistic Quantum Field Theory Problem Set 8 Due Friday, 09 December 2011 28. Unitarity and scattering longitudinal vector states. Massive vectors have three polarization states: two transverse and one longitudinal. However, massless vectors have only transverse polarization states. Through introducing scalar degreesoffreedom to a massless vector Lagrangian, we decouple the longitudinal modes from the transverse ones at energies large compared to the vector mass. However, when multiple selfinteracting vectors are given the same mass, Smatrix elements for longitudinal vector scattering grow without bound for energies parametrically larger than the vectormass. In this problem, we explore the tension between massive vectors and the unitarity of the Smatrix. a) Begin with a massive photon, L = 1 4 g 2 F μν F μν + v 2 ( A μ A μ ) . (1) The mass term is not invariant under local gauge transformation A μ → A μ + ∂ μ α ( x )....
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 '09
 ALEXANDERM.POLYAKOV
 Mass, Quantum Field Theory, Polarization, Aµ Aµ, polarization states

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