Gauge field Noether current density

It is useful for the following discussion to consider the symmetries of the Lagrangian (2.1) in order to analyse the conservation laws of a system characterised by (2.1) on the most general level, i.e. without further specifying F", and their consequences for the structure of a density functional approach to (2.1). We first consider continuous symmetries which in the field theoretical context are usually discussed on the basis of Noether s theorem (see e.g. [26, 28]). The most obvious symmetry of the Lagrangian (2.1), its gauge invariance (2.9), directly reflects current conservation,... 

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