Scalar field charge current density

Since the d Alembert operator is a Lorentz scalar, cf. Eq. (3.51), and the charge-current density fi has been shown to be a Lorentz 4-vector, it is immediately obvious that the gauge field also represents a Lorentz 4-vector and transforms according to Eq. (3.36) xmder Lorentz transformations. 

Vi2- If the value of the potential is known everywhere in space can be interpreted as a potential field (x,y,z), V is simply the voltage difference between two defined points in a wired electric circuit. is a scalar quantity [energy per charge = volt], the current density J is a space vector and has a current density vector field J(x,y,z). 

The magnetic resjwnse of diamagnetic atoms, molecules and clusters, i.e., typical quantum mechanical systems, can be effectively interpreted and visualized via the laws of classical electrodynamics, allowing for functions of position r which describe the electronic charge density p(r), a scalar property, and the electronic current density J(r), a vector field, evaluated by quantum mechanical methods. 

The results are thus entirely analogous to those obtained for the electric field the scalar moment of the electric charge density is simply replaced by the vector moment (torque) of the electric current density the density in each case may be either permanent or induced—(11.6.24) being formally similar to (11.6.26). 

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