Gauge Transformation
In physics a Gauge theory is a type of field theory in which the Lagrangian is invariant under certain 'Lie' group of local Transformation.Gauge Transformationis the english translation of German word 'Eichinvarianz' ,Where Eich means 'Gauge'. Classical Gauge Transformation in Electrodynamics: The Maxwell's equations in free space : $$ (1) \nabla.\overrightarrow{E} = \frac{\rho}{\epsilon_0} \text{ (Gauess's Law)}$$ $$(2) \nabla\text{.}\overrightarrow{B} = 0 \text{ (No Name i.e no existance of magnetic monopole)} $$ $$(3) \nabla\text{x}\overrightarrow{E}=\frac{\partial\overrightarrow{B}}{\partial{t}} \text{ (Farady's Law)} $$ $$ (4) \nabla\text{x}\overrightarrow{B} = \mu_0\overrightarrow{J}+\mu_0\epsilon_0\frac{\partial{\overrightarrow{E}}}{\partial {t}} \text{(Ampears Law with Maxwell's corrections)}$$ Where $$\mu_0$$ and $$\epsilon_0$$ are free space permitivity and free space permeability respectively. Suppose we h...