Lagrangian and Hamiltonian formalisms for relativistic dynamics of a charged particle with dipole moment
National Science Centre Kharkov Institute of Physics and Technology, Akademicheskaya 1, 61108, Kharkov, Ukraine
2 The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34100, Trieste, Italy
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.
© Springer-Verlag, 2005