Quadratic effective action for QED in D=2,3 dimensions - art. no. 125018

We calculate the effective action for quantum electrodynamics (QED) in D = 2,3 dimensions at the quadratic approximation in the gauge fields. We analy ze the analytic structure of the corresponding nonlocal boson propagators n onperturbatively in k/m. In two dimensions for any nonzero fermion mass, we end up with one massless pole for the gauge boson. We also calculate in D = 2 the effective potential between two static charges separated by a dista nce L and find it to be a linearly increasing function of L in agreement wi th the bosonized theory (massive sine-Gordon model). In three dimensions we find nonperturbatively in k/m one massive pole in the effective bosonic ac tion leading to screening. Fitting the numerical results we derive a simple expression for the functional dependence of the boson mass upon the dimens ionless parameter e(2)/m.