Exact invariants quadratic in the momentum for a particle in a three-dimensional electromagnetic field

Journal Article · Sun Apr 01 04:00:00 EST 1984 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526257· OSTI ID:5208151

Lewis, H R

For a Hamiltonian of the form H = (1)/(2) ( p-A(r,t))/sup 2/+V(r,t), the conditions on the scalar and vector potentials V(r,t) and A(r,t) have been found such that there exists an exact invariant that is quadratic in each component of the canonical momentum p. The invariant is written in the form I(r,p,t) = (1)/(2) (f/sub 2/(r,t)xp-f/sub 1/(r,t))/sup 2/+f/sub 0/(r,t), where f/sub 2/ is a nonsingular symmetric real dyad, f/sub 1/ is a real vector, and f/sub 0/ is a real scalar. For the cases in which f/sub 2/ is proportional to the unit dyad, or the vector potential is identically zero and f/sub 2/ commutes with the time derivative of f/sub 2/, all of the potentials that satisfy the conditions for such invariants to exist have been found explicitly and the invariants have been found in terms of the potentials. The derivation is a generalization of a method reported by Lewis and Leach for the corresponding one-dimensional problem. For the case in which the vector potential vanishes identically, the result is a generalization of a result found in three dimensions by Chandrasekhar. The results presented are applicable in plasma physics and stellar dynamics.

• Research Organization: Los Alamos National Laboratory, Los Alamos, New Mexico 87575
• OSTI ID: 5208151
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 25:4; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645400 -- High Energy Physics-- Field Theory
658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CANONICAL DIMENSION
DYNAMICS
ELECTROMAGNETIC FIELDS
HAMILTONIANS
LINEAR MOMENTUM
MATHEMATICAL OPERATORS
MECHANICS
PARTICLES
PLASMA
QUANTUM OPERATORS
SCALAR FIELDS
SCALE DIMENSION
STARS
THREE-DIMENSIONAL CALCULATIONS
USES
VECTOR FIELDS