Abstract
Periodic solutions of nonlinear field equations depending on a single degree of freedom are quantized canonically. The quantized excitations of nonlinear fields generalize the concepts of “photon” or “phonon” of linear fields, and satisfy characteristic equations. For example, the “quanta” of the sine-Gordon equation are Mathieu functions with a nonlinear energy spectrum. They take the place of the ordinary plane waves. It is suggested that these nonlinear quanta should be taken as building blocks for the quantization of nonlinear fields. Spinor-type quantized wave functions arise. Soliton solution is a limiting case. These quantized excitations may be observable.
Lectures given at NATO advanced Study Institute on Nonlinear Equations in Physics and Mathematics, Istanbul, August 1977
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© 1978 D. Reidel Publishing Company, Dordrecht, Holland
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Barut, A.O. (1978). Characteristic “Quanta” of Nonlinear Field Equations. In: Barut, A.O. (eds) Nonlinear Equations in Physics and Mathematics. NATO Advanced Study Institutes Series, vol 40. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9891-9_14
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DOI: https://doi.org/10.1007/978-94-009-9891-9_14
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