- #1
kof9595995
- 679
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What does it mean by "independent"(in gauge fixing of EM field)
In my textbook, it gives the Coulomb gauge [tex]\phi = 0,\nabla A = 0[/tex] and says they will kill two degrees of freedom of the four potential and leave two independent components. I understand [tex]\phi = 0[/tex] will kill one degree of freedom, but I'm not so sure about [tex] \nabla A = 0[/tex]. Usually the scenario is,let say we have 3 unknowns, and they are linked by a equation, such that given any two, the third unknown will be uniquely determined, that's what we called "kills a degree of freedom". However in [tex] \nabla A = 0[/tex], given [tex]{A_x},{A_y}[/tex], we will only know [tex]\frac{{\partial {A_z}}}{{\partial z}}[/tex], so A_z is not uniquely determined by A_x and A_y. So how should I interpret this?
In my textbook, it gives the Coulomb gauge [tex]\phi = 0,\nabla A = 0[/tex] and says they will kill two degrees of freedom of the four potential and leave two independent components. I understand [tex]\phi = 0[/tex] will kill one degree of freedom, but I'm not so sure about [tex] \nabla A = 0[/tex]. Usually the scenario is,let say we have 3 unknowns, and they are linked by a equation, such that given any two, the third unknown will be uniquely determined, that's what we called "kills a degree of freedom". However in [tex] \nabla A = 0[/tex], given [tex]{A_x},{A_y}[/tex], we will only know [tex]\frac{{\partial {A_z}}}{{\partial z}}[/tex], so A_z is not uniquely determined by A_x and A_y. So how should I interpret this?