Derivative expansion and the parity violating effective action for thermal(2+1)-dimensional QED at higher orders

Abstract

We systematically study induced higher order corrections to the parity violating part in thermal ${\mathrm{QED}}_{2+1},$ in the static limit, using the method of derivative expansion. We explicitly calculate the parity violating parts of the quadratic, cubic and the quartic terms (in fields) of the effective action which is linear in the magnetic field. We show that each of these actions can be summed, in principle, to all orders in the derivatives. However, such a structure is complicated and not very useful. On the other hand, at every order in the powers of the derivatives, we show that the effective action can also be summed to all orders in the ${A}_{0}$ fields. The resulting thermal parity violating actions can be expressed in terms of the leading order effective action in the static limit. We prove gauge invariance, both large and small of the resulting effective actions, within the framework of derivative expansion. Various other features of the theory are also brought out.