# A Canonical Transformation in Neoclassical Radiation Theory

## Abstract

There have been recenCt attempts^{(1–4)} to study radiation theory from a classical point of view. One of particular interest that has been investigated extensively is the formulation due to Jaynes and co-workers^{(5)} called the neoclassical theory. This theory can be developed from the Hamiltonian viewpoint from which equations of motion can be derived. For example, Maxwell’s equations form one set of these equations of motion where the driving currents are *c*-numbers formed by taking expectation values of the quantum operator currents. Much of the previous work has been devoted to examining the solutions of these equations. Here we discuss the formal Hamiltonian development with special emphasis on the freedom allowed by canonical transformations. In particular, we make explicit canonical transformations analogous to those used in quantum electrodynamics.^{(6–9)} For example, one such transformation gives a flexibility in the choice of the field **E** or **D** for the canonical momentum. This corresponds to the transformation from minimal coupling to a Hamiltonian in multipolar form. Despite the classical nature of the Hamiltonian, a detailed analysis of the transformation shows that the Schrödinger character of the underlying dynamics requires closure relations and other sum rules that reflect basic quantum behavior.

## Keywords

Quantum Electrodynamic Canonical Transformation Transition Moment Canonical Momentum Neoclassical Theory## Preview

Unable to display preview. Download preview PDF.

## References

- 1.
- 2.
- 3.
- 4.For a general discussion see
*Coherence and Quantum Optics*,Eds. L. Mandel and E. Wolf, Plenum, New York (1973).Google Scholar - 5.E. T. Jaynes, reference
**4**, p. 35.Google Scholar - 6.E. A. Power and S. Zienau,
*Philos. Trans. R. Soc. London Ser. A***251**, 427 (1959).MathSciNetADSzbMATHCrossRefGoogle Scholar - 7.
- 8.M. Babiker, E. A. Power, and T. Thirunamachandran,
*Proc. R. Soc. London Ser. A***338**, 235 (1974).MathSciNetADSCrossRefGoogle Scholar - 9.E. A. Power and T. Thirunamachandran,
*Am. J. Phys*.**46**, 370 (1978).MathSciNetADSCrossRefGoogle Scholar - 10.
- 11.
- 12.
- 13.
- 14.A. A. Maradudin, E. W. Montroll, and G. W. Weiss,
*Solid State Phvs. Supp*.**3**, 138 (1963)MathSciNetGoogle Scholar