A hidden generalized gauge symmetry of a cutoff QED is used to show the renormalizability of QED. In particular, it is shown that corresponding Ward identities are valid all along the renormalization group flow. The exact Renormalization Group flow equation corresponding to the effective action of a cutoff λϕ 4 theory is also derived. Generalization to any gauge group is indicated.
The mass spectrum of the noncommutative QED in two-dimensional Euclidean R 2 space is derived first in a perturbative approach at one-loop level and then in a nonperturbative approach using the equivalent bosonized noncommutative effective action. It turns out that the mass spectrum of noncommutative QED in two dimensions reduces to a single noninteracting meson with mass M γ = g √ π , as in commutative Schwinger model.
The photon self-energy of the noncommutative Schwinger model at two- and three-loop order is analyzed. It is shown that the mass spectrum of the model does not receive any correction from the noncommutativity parameter () at these orders. Also it remains unchanged to all orders. The exact one-loop effective action for the photon is also calculated.
The noncommutative (NC) massive quantum electrodynamics in 2 + 1 dimensions is considered. We show explicitly that the one-loop effective action arising from the integrating out the fermionic fields leads to the ordinary NC Chern-Simons and NC Maxwell action at the long wavelength limit (large fermion mass). In the next to leading order, the higher-derivative contributions to NC Chern-Simons are obtained. Moreover, the gauge invariance of the outcome action is carefully discussed. We then consider the higher-derivative modification into the pure NC Chern-Simons Lagrangian density and evaluate the one-loop correction to the pole of the photon propagator.
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