Potentials and Gauge Symmetry

After introduction of these potentials the homogeneous Maxwell equations (2.96) and (2.97) are therefore identically satisfied due to general properties of differential vector calculus (cf. appendix A.l). The dynamical behavior of the potentials is determined by the inhomogeneous Maxwell equations, which in terms of the potentials read 

Equations (2.127)-(2.129) are equivalent in all respects to Maxwell s four original equations in terms of E and B. 

By inspection of Eq. (2.127) we find that the scalar and vector potentials defining the electric and magnetic fields are not unique but bear a certain de- 

Nevertheless, the introduction of the potentials (p and A reduces the number of fields, and they are to be considered as the dynamical variables of the theory. Owing to the gauge symmetry given by Eqs. (2.130) and (2.131), it is obvious that Maxwell s theory of electromagnetism features redundant degrees of freedom which will seriously hamper its quantization in chapter 7. The potentials cp and A themselves are denoted gauge potentials. 

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