Data di Pubblicazione:
2008
Citazione:
On the physical applications of hyper-Hamiltonian dynamics / G. Gaeta, M.A. Rodriguez. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 41:17(2008 May), pp. 175203.175203-1-175203.175203-16.
Abstract:
An extension of Hamiltonian dynamics, defined on hyper-Kahler manifolds (‘hyper-Hamiltonian dynamics’) and sharing many of the attractive features of standard Hamiltonian dynamics, was introduced in previous work. In this paper, we discuss applications of the theory to physically interesting cases, dealing with the dynamics of particles with spin 1/2 in a magnetic field, i.e.
the Pauli and the Dirac equations. While the free Pauli equation corresponds to a hyper-Hamiltonian flow, it turns out that the hyper-Hamiltonian description of the Dirac equation, and of the full Pauli one, is in terms of two commuting
hyper-Hamiltonian flows. In this framework one can use a factorization principle discussed here (which is a special case of a general phenomenon
studied by Walcher) and provide an explicit description of the resulting flow.
On the other hand, by applying the familiar Foldy–Wouthuysen and Cini–Tousheck transformations (and the one recently introduced by Mulligan) which
separate—in suitable limits—the Dirac equation into two equations, each of these turn out to be described by a single hyper-Hamiltonian flow. Thus the hyper-Hamiltonian construction is able to describe the fundamental dynamics for particles with spin.
Tipologia IRIS:
01 - Articolo su periodico
Elenco autori:
G. Gaeta, M.A. Rodriguez
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