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Higher order approximation of the Dirac and Dirac-Pauli Hamiltonians in the Foldy-Wouthuysen representation | | Tsung-Wei Chen
; Dah-Wei Chiou
; | | Date: |
14 Nov 2013 | | Abstract: | The classical relativistic motion of a charged spin particle is governed by
the classical Hamiltonian, which is the sum of classical relativistic
Hamiltonian and Thomas-Bargmann-Michel-Telegdi (T-BMT) Hamiltonian. In the
previous work, it has bee shown that, in the low-energy/weak-field limit up to
the order of $1/m^8$ ($m$ is the particle’s mass), the Dirac-Pauli Hamiltonian
in the Foldy-Wouthuysen representation may be consistent with the classical
Hamiltonian. In this paper, we investigate the Foldy-Wouthuysen representation
of the Dirac and Dirac-Pauli Hamiltonians by using Kutzelnigg’s diagonalization
method. We show that the Kutzelnigg diagonalization method can be further
simplified if nonlinear effects of static and homogeneous electromagnetic
fields are neglected. Up to the order of $1/m^{14}$, we find that the
Foldy-Wouthuysen transformed Dirac Hamiltonian is in agreement with the
classical Hamiltonian with the gyromagnetic ratio given by $g=2$. Furthermore,
we also show that, up to the order of $1/m^{14}$, the Foldy-Wouthuysen
transformed Dirac-Pauli Hamiltonian agrees with the classical Hamiltonian with
$g
eq2$. | | Source: | arXiv, 1311.3432 | | Services: | Forum | Review | PDF | Favorites | |
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