E S Santos et al 2004 J. Phys. A: Math. Gen. 37 9771 doi:10.1088/0305-4470/37/41/011
E S Santos1,2, M de Montigny1,3, F C Khanna1,4 and A E Santana5
Show affiliationsWe construct non-relativistic Lagrangian field models by enforcing Galilean covariance with a (4, 1) Minkowski manifold followed by a projection onto the (3, 1) Newtonian spacetime. We discuss scalar, Fermi and gauge fields, as well as interactions between these fields, preparing the stage for their quantization. We show that the Galilean covariant formalism provides an elegant construction of the Lagrangians which describe the electric and magnetic limits of Galilean electromagnetism. Similarly we obtain non-relativistic limits for the Proca field. Then we study Dirac Lagrangians and retrieve the Lévy-Leblond wave equations when the Fermi field interacts with an Abelian gauge field.
11.10.Ef Lagrangian and Hamiltonian approach
81T70 Quantization in field theory; cohomological methods (See also 58D29)
Issue 41 (15 October 2004)
Received 13 March 2004, in final form 2 September 2004
Published 29 September 2004
E S Santos et al 2004 J. Phys. A: Math. Gen. 37 9771
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Vladislav Popkov et al 2008 J. Phys. A: Math. Theor. 41 432002
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