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Photon polarization tensor and gauge dependence in three-dimensional quantum electrodynamics

1992; American Physical Society; Volume: 46; Issue: 6 Linguagem: Inglês

10.1103/physrevd.46.2695

1538-4500

Conrad J. Burden, J. Praschifka, Craig D. Roberts,

Quantum Information and Cryptography

We calculate the three-dimensional QED (${\mathrm{QED}}_{3}$) photon polarization tensor using dressed fermion propagators and a fermion-photon vertex that satisfies the Ward-Takahashi identity. Irrespective of the structural details of the transverse part of the fermion-photon vertex the photon remains massless; i.e., there is no photon mass generation in the manner of the Schwinger mechanism. Our calculation suggests that ${\mathrm{QED}}_{3}$ is confining when the polarization tensor is calculated using a dressed fermion propagator and fermion-photon vertex. The gauge parameter dependence of the fermion propagator, fermionphoton vertex, and photon polarization tensor is discussed in connection with the Landau-Khalatnikov gauge transformation laws.