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- W1978952226 abstract "For a Hamiltonian of the form H= (1)/(2) ( p−A(r,t))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) (f2(r,t)⋅p−f1(r,t))2+f0(r,t), where f2 is a nonsingular symmetric real dyad, f1 is a real vector, and f0 is a real scalar. For the cases in which f2 is proportional to the unit dyad, or the vector potential is identically zero and f2 commutes with the time derivative of f2, 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." @default.
- W1978952226 created "2016-06-24" @default.
- W1978952226 creator A5046018851 @default.
- W1978952226 date "1984-04-01" @default.
- W1978952226 modified "2023-09-27" @default.
- W1978952226 title "Exact invariants quadratic in the momentum for a particle in a three-dimensional electromagnetic field" @default.
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- W1978952226 doi "https://doi.org/10.1063/1.526257" @default.
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