The notion of configurational force in mechanics and thermomechanics can be readily extended to electromagnetic elastic materials. By invariance arguments and through variational procedures, the Maxwell equations are transformed into a Lagrangian (or material) form and thus consistently coupled with the mechanical balance laws. In this context, the configurational forces and momenta depend also on the electromagnetic fields and specifically on the Lagrangian electromagnetic potentials. The question then arises as to whether the classical gauge conditions are still appropriate to the Lagrangian potentials. Eventually, gauge transformations for these potentials are examined for the full set of equations of interest.
1. Trimarco, C. and Maugin, G. A. Material mechanics of electromagnetic bodies. In Configurational Mechanics of Materials. CISM courses and lectures, No. 427, Springer, Wien, 2001, 129–172.
https://doi.org/10.1007/978-3-7091-2576-2_3
2. Maugin, G. A. and Trimarco, C. Elements of field theory in inhomogeneous and defective materials. In Configurational Mechanics of Materials. CISM courses and lectures, No. 427, Springer, Wien, 2001, 55–128.
https://doi.org/10.1007/978-3-7091-2576-2_2
3. Trimarco, C. A Lagrangian approach to electromagnetic bodies. Technische Mech., 2002, 22, 175–180.
4. Maugin, G. A. Material Inhomogeneities in Elasticity. Chapman and Hall, London, 1993.
https://doi.org/10.1007/978-1-4899-4481-8
5. Gurtin, M. E. Configurational Forces as Basic Concepts of Continuum Physics. Springer Verlag, New York, 2000.
6. Kienzler, R. and Herrmann, G. Mechanics in Material Space. Springer, Berlin, 2000.
https://doi.org/10.1007/978-3-642-57010-0
7. Trimarco, C. The total kinetic energy of an electromagnetic body. Phil. Mag., 2005, 85, 4277–4287.
https://doi.org/10.1080/14786430500363817
8. Trimarco, C. Material electromagnetic fields and material forces. Arch. Applied Mechanics, 2007, 77, 177–184.
https://doi.org/10.1007/s00419-006-0056-2
http//maecourses.ucsd.edu/symi/otherpapers.html
9. Becker, R. and Sauter, F. Electromagnetic Interactions, Vol. 2. Blackie & Sons, London, 1964.
10. Landau, L. and Lifschitz, E. Méchanique Quantique, 3rd edition. MIR Edition, 1974.
11. Kittel, C. Introduction to Solid State Physics, 6th edition. John Wiley & Sons, New York, 1986.
12. Truesdell, C. A. and Noll, W. The nonlinear field theory of mechanics. In Handbuch der Physik, Bd. III/3 (Flügge, S., ed.). Springer, Berlin, 1965, 1–602.
https://doi.org/10.1007/978-3-642-46015-9_1
13. Schoeller, H. and Thellung, A. Lagrangian formalism and conservation law for electrodynamics in nonlinear elastic dielectrics. Ann. Physics, 1992, 220, 18–39.
https://doi.org/10.1016/0003-4916(92)90324-F
14. Nelson, D. F. Electric, Optic and Acoustic Interactions in Dielectrics. John Wiley, New York, 1979.
15. Jackson, J. D. Classical Electrodynamics. J. Wiley & Sons, New York, 1962.
https://doi.org/10.1063/1.3057859
16. Jackson, J. D. Historical roots of gauge invariance. Rev. Modern Phys., 2001, 73, 663–681.
https://doi.org/10.1103/RevModPhys.73.663
17. Jackson, J. D. From Lorenz to Coulomb and other explicit gauge transformations. Am. J. Phys., 2002, 70, 917–928.
https://doi.org/10.1119/1.1491265
18. Brill, O. L. and Goodman, B. Causality in the Coulomb gauge. Am. J. Phys., 1967, 35, 832–837.
https://doi.org/10.1119/1.1974261
19. Goldstein, H. Classical Mechanics, 12th edition. Addison-Wesley, Reading, Mass, 1980.
20. Henneau, M. and Teteilboim, C. Quantization of Gauge Systems. Princeton University Press, Princeton, NJ, 1992.
21. Aharonov, Y. and Bohm, D. Significance of electromagnetic potentials in the quantum theory. Phys. Rev., Series II, 1959, 115, 485–491.
https://doi.org/10.1103/PhysRev.115.485
22. Maugin, G. A. Irreversible thermodynamics of deformable superconductors. C. R. Acad. Sci. Paris, Série II, 1992, 314, 889–894.
