1 Notations

I am using the same notations as in [3] and [2]. 2 Temporal gauge-various approaches Obviously the temporal gauge ¯ q i = a i = const or in QED: A 0 = a ∈ R (1) is not a canonical gauge as it does not fulfill eq. (1.59) of [7]. However, we do not need a canonical gauge in order to fix our gauge degrees of freedom. There exist various other gauges (e.g. derivative gauges, multiplier gauges etc.). The reason for the introduction of such gauges and its justification are developed in section 3.4 of [7]. The quantization of such theories can be shown to be consistent in the frame of BRST theory only. Therefore, unfortunately, at the moment I am not able to go into details. 2.1 The " direct " approach see [3]-but I admit that this approach may leave some open questions. 2.2 The " adding a gauge fixing field " approach The idea is to introduce the gauge fixing directly in the Lagrangian: L → L + B (¯ q i − a i) (2) with some (non-dynamical) additional field B. In fact, this can already be done for QED and we will treat it as a toy model: