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Non-relativistic QED

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Part of the SpringerBriefs in Molecular Science book series (BRIEFSMOLECULAR)

Abstract

A brief presentation is given of the construction of the theory of molecular QED. This is done by first writing a classical Lagrangian function for a collection of non-relativistic charged particles coupled to an electromagnetic field. After selecting the Coulomb gauge, Hamilton’s principle is invoked and the Lagrangian is substituted into the Euler-Lagrange equations of motion and shown to lead to the correct dynamical equations. These are Newton’s second law of motion with added Lorentz force law electric and magnetic field dependent terms, and the wave equation for the vector potential in the presence of sources. Canonically conjugate particle and field momenta are then evaluated, from which the Hamiltonian is derived. Elevation of classical variables to quantum operators finally yields the molecular QED Hamiltonian, which is expressed in minimal-coupling and multipolar forms. In the QED formulation, the electromagnetic field is described as a set of independent simple harmonic oscillators. Elementary excitations of the field, the photons, emerge automatically on quantisation.

Keywords

Lagrangian Polarisation Magnetisation Minimal-coupling Hamiltonian Canonical transformation Multipolar Hamiltonian Perturbation theory 

References

  1. 1.
    Schwinger JS (ed) (1958) Selected papers on quantum electrodynamics. Dover, New YorkGoogle Scholar
  2. 2.
    Goldstein H (1960) Classical mechanics. Addison-Wesley, Reading, MAGoogle Scholar
  3. 3.
    Dirac PAM (1958) The principles of quantum mechanics. Clarendon, OxfordGoogle Scholar
  4. 4.
    Morse PM, Feshbach H (1953) Methods of theoretical physics. McGraw-Hill, New YorkGoogle Scholar
  5. 5.
    Jackson JD (1975) Classical electrodynamics. Wiley, New YorkGoogle Scholar
  6. 6.
    Power EA (1964) Introductory quantum electrodynamics. Longmans, LondonGoogle Scholar
  7. 7.
    Born M, Heisenberg W, Jordan P (1926) Zur quantenmechanik II. Z Phys 35:557CrossRefGoogle Scholar
  8. 8.
    Jeans JH (1905) On the partition of energy between matter and aether. Philos Mag 10:91CrossRefGoogle Scholar
  9. 9.
    Craig DP, Thirunamachandran T (1998) Molecular quantum electrodynamics. Dover, New YorkGoogle Scholar
  10. 10.
    Salam A (2010) Molecular quantum electrodynamics. Wiley, HobokenGoogle Scholar
  11. 11.
    Born M, Oppenheimer JR (1927) Zur quantentheorie der molekeln. Ann Phys 84:457CrossRefGoogle Scholar
  12. 12.
    Schrödinger E (1926) Der stetige Übergang von der Mikro-zur Makromechanik. Naturwissenschaften 14:664CrossRefGoogle Scholar
  13. 13.
    Milonni PW (1994) The quantum vacuum. Academic Press, San DiegoGoogle Scholar
  14. 14.
    Power EA (1978) A review of canonical transformations as they affect multiphoton processes. In: Eberly JH, Lambropoulos P (eds) Multiphoton processes. Wiley, New York, pp 11–46Google Scholar
  15. 15.
    Power EA, Zienau S (1959) Coulomb gauge in non-relativistic quantum electrodynamics and the shape of spectral lines. Phil Trans Roy Soc London A251:427CrossRefGoogle Scholar
  16. 16.
    Woolley RG (1971) Molecular quantum electrodynamics. Proc Roy Soc London A321:557CrossRefGoogle Scholar
  17. 17.
    Babiker M, Power EA, Thirunamachandran T (1974) On a generalisation of the Power-Zienau-Woolley transformation in quantum electrodynamics and atomic field equations. Proc Roy Soc London A338:235CrossRefGoogle Scholar
  18. 18.
    Power EA, Thirunamachandran T (1980) The multipolar Hamiltonian in radiation theory. Proc Roy Soc London A372:265CrossRefGoogle Scholar
  19. 19.
    Cohen-Tannoudji C, Dupont-Roc J, Grynberg G (1989) Photons and atoms. Wiley, New YorkGoogle Scholar
  20. 20.
    Healy WP (1982) Non-relativistic quantum electrodynamics. Academic Press, LondonGoogle Scholar
  21. 21.
    Compagno G, Passante R, Persico F (1995) Atom-field interactions and dressed atoms. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  22. 22.
    Göppert-Mayer M (1931) Über elementarakte mit zwei quantensprüngen. Ann Phys Leipzig 9:273CrossRefGoogle Scholar
  23. 23.
    Power EA, Thirunamachandran T (1978) On the nature of the Hamiltonian for the interaction of radiation with atoms and molecules: (e/mc)p.A, −μ.E, and all that. Am J Phys 46:370CrossRefGoogle Scholar

Copyright information

© The Author(s)  2016

Authors and Affiliations

  1. 1.Department of ChemistryWake Forest UniversityWinston-SalemUSA

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