On the Significance of Density of an Electrically Charged Quantum Particle

Expressions of a conserved 4-current and its density are examined in cases of electrically charged quantum particles. It is proven that the Noether theorem cannot be regarded as a sufficient condition that yields a consistent expression of a conserved 4-current, because electromagnetic interactions pose further constraints. A mathematical analysis shows that the Dirac linear equation yields a consistent expression for a 4-current. In contrast, second order quantum equations, such as the Klein-Gordon equation of an electrically charged scalar particle and the electroweak equation of the W± vector particles do not provide a consistent expression for a conserved 4-current that adequately describes electromagnetic interactions.