Abstract
A general account of the interaction of electric charges with electromagnetic radiation is presented, the charges being treated in the non-relativistic approximation. The two main approaches in the literature, based on either the potentials of the electromagnetic field (‘minimal coupling’) or the polarization fields of the charges (e.g., the ‘multipolar Hamiltonian’) are presented in a unified framework, that characterizes them as simply different viewpoints of the same general structure. This structure is very suitable for a discussion of the gauge invariance of the theory. The final quantum mechanical Hamiltonian presented here has recently been shown to provide the basis for a proof of the gauge invariance of its associated S-matrix to all orders of perturbation theory, provided the S-matrix is taken on the energy-shell. Some outstanding problems are described briefly.
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References
Lorentz, H.A.: The Theory of the Eletron; 2nd Ed., Teubner, Leipzig, 1916.
Hirst, L.L.: Rev. Mod. Phys., 69 (1997) 607–627.
Schwinger, J.: Particles, Sources and Fields, p. 260, Addison-Wesley, 1970.
Woolley, RG.: Ann. Inst. Henri Poincaré, 23A (1975) 365–378.
Belinfante, F.J.: Phys. Rev. 128 (1962) 2832–2837.
Power, E.A., and Zienau, S.: Phil. Trans. Roy. Soc. (London), A251 (1959) 427–454.
Woolley, R.G.: Proc. Roy. SOC. (London), A321 (1971) 557–572.
London R.: Quantum Theory of Light, 2nd Edition, Oxford University Press, 1983.
Cohen-Tannoudji, C.. Dupont-Roc, J., and Grynberg: G.: Photons and Atoms: Introduction to Quantum Electrodynamics, Wiley, New York, 1989.
Power. E.A.: Introductory Quantum Electrodynamics, Longmans, Harlow, 1964.
Dirac, P.A.M.: Ann. Inst. Henri Poincaré, 13 (1952) 1–42.
Dirac, P.A.M.: Lectures on Quantum Mechanics, Academic Press, 1964.
Weinberg, S.: The Quantum Theory of Fields, Vol. 1, Foundations, Cambridge University Press, 1995.
Woolley, R.G.: Adv. Chem. Phys., 33 (1975) 153–233.
Atkins, P.W., and Woolley, RG.: Proc. Roy. Soc. (London), A319 (1970) 549–563.
Roman, P: Advanced Quantum Theory, Addison-Wesley Publishing Co. Inc., Reading, Mass. 1965.
Berestetskii, V.B.. Lifshitz, E.M.; and Pitaevskii, L.P.: Relativistic Quantum Theory, Vol. 4 of Course of Theoretical Physics, Part 1, §73: Pergamon Press, Oxford, 1971.
Atkins, P.W. and Barron, L.D.: Proc. Roy. Soc. (London), A304 (1968) 303–317.
Atkins, P.W. and Barron, L.D.: Proc. Roy. Soc. (London), A306 (1968) 119–134.
Woolley, R.G.: Int. J. Quant. Chem. (1999), in the press.
Woolley, R.G.: Mol. Phys., 94 (1998) 409–416.
Healy, W.P.: Phys. Rev.: A16 (1977) 1568.
Weisskopf, V., and Wigner, E.P.: Z. Physik, 63 (1930) 54; 65 (1930) 18.
Heitler, W.: The Quantum Theory of Radiation, 3rd Edition, Oxford University Press (1954).
Lamb, W.E.: Phys Rev., 85 (1952) 259.
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Woolley, R.G. (2000). On Gauge Invariance and Molecular Electrodynamics. In: Maruani, J., Minot, C., McWeeny, R., Smeyers, Y.G., Wilson, S. (eds) New Trends in Quantum Systems in Chemistry and Physics. Progress in Theoretical Chemistry and Physics, vol 7. Springer, Dordrecht. https://doi.org/10.1007/0-306-46950-2_1
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DOI: https://doi.org/10.1007/0-306-46950-2_1
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