Abstract.
The Lagrangian and Hamiltonian formulations for the relativistic classical dynamics of a charged particle with dipole moment in the presence of an electromagnetic field are given. The differential conservation laws for the energy-momentum and angular momentum tensors of a field and particle are discussed. The Poisson brackets for basic dynamic variables, which form a closed algebra, are found. These Poisson brackets enable us to perform the canonical quantization of the Hamiltonian equations that leads to the Dirac wave equation in the case of spin 1/2. It is also shown that the classical limit of the squared Dirac equation results in equations of motion for a charged particle with dipole moment obtained from the Lagrangian formulation. The inclusion of gravitational field and non-Abelian gauge fields into the proposed formalism is discussed.
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Received: 4 June 2005, Published online: 27 July 2005
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Peletminskii, A., Peletminskii, S. Lagrangian and Hamiltonian formalisms for relativistic dynamics of a charged particle with dipole moment. Eur. Phys. J. C 42, 505–517 (2005). https://doi.org/10.1140/epjc/s2005-02336-4
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DOI: https://doi.org/10.1140/epjc/s2005-02336-4