Summary
The conventional way to set up a decent looking theory for interacting elementary particles is to take some set of classical fields, satisfying simple, polynomial field equations. These equations should be compatible with an extremum principle: they are taken to be the Euler-Lagrange equations generated by some Lagrange function L of the fields. One then “quantizes” the theory by replacing Poisson brackets by commutators.
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References
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© 1987 Plenum Press, New York
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’t Hooft, G. (1987). Quantum Black Holes. In: Lévy, M., Basdevant, JL., Jacob, M., Speiser, D., Weyers, J., Gastmans, R. (eds) Particle Physics. NATO ASI Series, vol 150. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1877-4_16
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DOI: https://doi.org/10.1007/978-1-4613-1877-4_16
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