What is the Magnetic Moment of the Electron?

Abstract:

 Because of infrared effects the charged sectors of QED contain no eigenstates of the mass operator. The electron is therefore not definable as a Wigner particle. There exists no sharp, unambiguous, definition of the notion of a 1-electron state. The assignment of a fixed value of the magnetic moment – or similar quantities – to the electron is therefore at first problematic. It is not clear a priori that such a notion is meaningful. Conventionally this problem is solved by first calculating the desired quantity in an IR-regularized theory and then removing the regularization. If this method yields a finite value, that is considered sufficient proof of its soundness. This is clearly less than satisfactory. Here we propose a more convincing way of defining the intrinsic magnetic moment of the electron, which does not use any regularizations and is not based on an interaction with external fields. A pseudostatic 1-electron state is defined in a phenomenological way. Its magnetic moment, as defined here, does not depend on the unavoidable ambiguities inherent in this definition. The method leads to the same analytic expression as the conventional approach, thus preserving the excellent agreement between theory and experiment.