On the Hamiltonian of a System of Charges Moving in a Magnetic Field

摘要

The Hamiltonian for a system of charges moving in a static magnetic field is considered. It was brought to light that the magnetic energy, introduced commonly in the system, leads to a total annihilation of the kinetic energy of the system in the plane perpendicular to the magnetic field. Thus both the magnetic energy and the coincident momenta of charges terms disappear from the Hamiltonian, This has not been noted to date. The partial derivative of the Hamiltonian with respect to the magnetic field or to the considered momenta vanishes, whereupon the canonical transformations, a statistical sum, and the magnetic moment of the system turn out to be illusory. It is noted that the Hamiltonian function cannot be applied to the charges moving in a magnetic field at all because in this case the system becomes nonholonomic.