Charged particles with electromagnetic interactions and U(1)-gauge theory: Hamiltonian and Lagrangian formalisms

Journal Article · Fri Jun 15 00:00:00 EDT 1984 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.29.2814· OSTI ID:6569173

Beckers, J; Hussin, V

The motion of charged particles in external electromagnetic fields is reviewed with the purpose of determining the whole set of constants of motion. The Johnson-Lippmann results concerning the interaction with a constant magnetic field are taken as the starting point of the study. Our results are obtained through simple group-theoretical arguments based essentially on extended Lie algebras associated with the kinematical group of the (constant) electromagnetic field involved in the interaction. Nonrelativistic Schroedinger (or Pauli) and relativistic Dirac Hamiltonians are considered. The corresponding Lagrangian densities are then studied when the charged particles move in arbitrary electromagnetic fields. Through Noether's theorem, we get the constants of motion when coordinate and gauge transformations are combined. These results complete the U(1)-gauge theory and relate the works of Bacry, Combe, and Richard and of Jackiw and Manton when external gauge fields are considered. These developments enhance the minimal-coupling principle, the U(1)-gauge theory, and Noether's theorem.

• Research Organization: Physique Theorique et Mathematique, Universite de Liege, Institut de Physique au Sart Tilman, B-4000 Liege 1, Belgium
• OSTI ID: 6569173
• Journal Information: Phys. Rev. D; (United States), Vol. 29:12
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CHARGED PARTICLES
ELECTROMAGNETIC INTERACTIONS
GAUGE INVARIANCE
HAMILTONIANS
LAGRANGIAN FUNCTION
MAGNETIC FIELDS
SCHROEDINGER EQUATION
U-1 GROUPS
BASIC INTERACTIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
INTERACTIONS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
SYMMETRY GROUPS
U GROUPS
WAVE EQUATIONS
645202* - High Energy Physics- Particle Interactions & Properties-Theoretical- Electromagnetic Interactions & Properties
645400 - High Energy Physics- Field Theory