One-loop photon’s effective action in the noncommutative scalar QED3

Abstract

In this paper, we consider the evaluation of the effective action for photons coupled to charged scalar fields in the framework of a (2 + 1)-dimensional noncommutative spacetime. In order to determine the noncommutative Maxwell Lagrangian density, we follow a perturbative approach, by integrating out the charged scalar fields, to compute the respective graphs for the vev's AA , AAA and AAAA . Surprisingly, it is shown that these contributions are planar and that, in the highly noncommutative limit, correspond to the Maxwell effective action and its higher-derivative corrections. It is explicitly verified that the one-loop effective action is gauge invariant, as well as under discrete symmetries: parity, time reversal and charge conjugation. Moreover, a comparison of the main results with the noncommutative QED 3 is established. In particular, the main difference is the absence of parity violating terms in the photon's effective action coming from integrating out the charged scalar fields. * ghasemkhani@ipm.ir †

Energy level splitting of a 2D hydrogen atom with Rashba coupling in non-commutative space

“… where E n 0 ( ) denotes the energy spectrum of the 2D hydrogen atom in the absence of the Rashba term (equation ( 4)) and m is the magnetic quantum number. A glance at equation (12) reveals that the energy spectrum of our system is comparable with the results reported in [17] where the energy spectrum of 2D hydrogen with Rashba coupling is evaluated. In addition, if we set l » -10 R 4 , in the natural unit, we then find the splitting energy in an order of meV which is compatible with other low-dimensional systems.…”

“…Techniques from NC space have played a major role in low-dimensional physics such as the quantum Hall effect [9] and the gravitational quantum well [10]. There have been many phenomenological consequences of the NC theory in different physical problems in both quantum mechanics [11] and quantum field theory [12] frameworks.…”