# Unified View of Spontaneous Emission in Several Theories of Radiation

Chapter

## Abstract

Consider the model classical field theory described by the Lagrangian density ℒ( Evidently, ℒ(

**x**,*t*):$$
\mathcal{L}\left( {x,t} \right) = \psi *\left( {x,t} \right)\left\{ {i\hbar \frac{\partial }
{{\partial t}} - \frac{1}
{{2m}}\left[ {\frac{\hbar }
{i}\nabla - \frac{e}
{c}A\left( {x,t} \right)} \right] - V\left( x \right)} \right\}\psi \left( {x,t} \right) + \frac{1}
{{8\pi }}\left\{ {\left[ {\frac{1}
{c}\dot A\left( {x,t} \right)} \right]^2 - \left[ {\nabla \times A\left( {x,t} \right)} \right]^2 } \right\}$$

(1)

**x**) is the beginning of a theory of the interaction of the fields*ψ*and**A**. There are several free parameters in the theory:*ℏ, m, e, c*.## Keywords

Frequency Shift Spontaneous Emission Conjugate Momentum Unify View Interpretive Framework
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## References and Notes

- 1.By classical we mean that none of the interpretive framework of quantum field theory is involved, and that the dynamical fields are simple mathematical functions that commute everywhere and at all times with each other. Another discussion of possible consequences of (I) and (4) has been given by J. H. Eberly, in
*Laser Photochemistry*,*Tunable Lasers*,*and Other Topics*,Eds. S. F. Jacobs*et al*.,Addison-Wesley, Reading, Massachussetts (1976), p. 421.Google Scholar - 2.V. F. Weisskopf and E. Wigner,
*Z. Phys*. 63, 54 (1930). See also Section 28 of G. Källen,*Quantum Electrodynamics*, translated by C. K. Iddings and M. Mizushima, Springer, Heidelberg (1972).Google Scholar - 3.
- 4.S. B. Lai, Ph.D. Thesis, University of Rochester (1976).Google Scholar
- See also P. Avan, C. CohenTannoudji, J. Dupont-Roc, and C. Fabre,
*J. Phys. (Paris)***37**, 993 (1976)CrossRefGoogle Scholar - J. Dupont-Roc, C. Fabre, and C. Cohen-Tannoudji,
*J. Phys. B***11**, 563 (1978).ADSCrossRefGoogle Scholar - 5.P. W. Milonni,
*Phys. Rep*. 25, 1 (1976)ADSCrossRefGoogle Scholar - J. H. Eberly, reference 1; J. H. Eberly, in
*Particles and Fields 1974*, Ed. C. E. Carlson, American Institute of Physics, New York (1974).Google Scholar - 6.K. Wôdkiewicz and J. H. Eberly,
*Ann. Phys*. (New York) 101, 574 (1976), and references therein.Google Scholar - 7.
- P. W. Milonni, J. R. Ackerhalt, and W. A. Smith,
*Phys. Rev. Leu*.**31**, 958 (1973).ADSCrossRefGoogle Scholar - 8.
- 9.See E. T. Jaynes, Microwave Laboratory Report No. 502, Stanford University, Stanford (1958).Google Scholar
- 10.E. T. Jaynes, in
*Coherence and Quantum Optics*, Eds. L. Mandel and E. Wolf, Plenum, New York (1973), p. 35.CrossRefGoogle Scholar - 11.E. T. Jaynes, in
*Quantum Electronics*,Ed. C. H. Townes, Columbia University Press, New York (1960), p. 288. The Hamiltonian form of our field theory has close parallels with this earlier development.Google Scholar - 12.L. Mandel, in
*Progress in Optics*,Vol. 13, Ed. E. Wolf, North-Holland, Amsterdam (1975). See also P. W. Milonni, ref. 5 above.Google Scholar - 13.Our theory is obviously based directly on Jaynes’ NCT. What we call NED may well be identical with NCT, but it should be Jaynes who says so.Google Scholar
- 14.J. R. Ackerhalt, J. H. Eberly, and P. L. Knight, in
*Coherence and Quantum Optics*, Eds. L. Mandel and E. Wolf, Plenum, New York (1973), p. 635.CrossRefGoogle Scholar - See also the remarks of E. T. Jaynes, p. 68–69 of the same volume, and L. Allen and J. H. Eberly,
*Optical Resonance and Two-Level Atoms*, Wiley, New York (1975), Section 7. 4.Google Scholar

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