Abstract
The magnetic top is defined by the property that the external magnetic field B couples to the angular vecolity ω, as distinct from the top whose magnetic moment is a body-fixed vector. This allows one to construct a “gauge” theory of the top where the canonical angular momentum, s, is analogous to the canonical momentum of the point particle and the B field plays the role of the gauge potential. The magnetic top has four constants of motion so that Lagrange equations for Euler angles ϑ, ϕ, χ (which define the orientation of the top) are integrable and are solved here. Although the Euler angles perform complicated motions, the canonical angular momentum s, interpreted as spin, obeys precisely a simple precession equation. The Poisson brackets of s i allow us further to make an unambiguous quantization of spin, leading to the Pauli spin Hamiltonian. The use of canonical angular momentum alleviates the ambiguity in the ordering of the variables ϑ, ϕ, χ, p ϑ , p ϕ , p χ in the Hamiltonian. A detailed gauge theory of the asymmetric magnetic top is also given.
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