Quantization of Nonlinear Systems
- 1 November 1960
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 1 (6) , 468-488
- https://doi.org/10.1063/1.1703683
Abstract
A direct method of quantization, applicable to a given nonlinear hyperbolic partial differential equation, is indicated. From such classical equations alone, without a given Lagrangian or Hamiltonian, or a priori linear reference system such as a bare or incoming field, a quantized field is constructed, satisfying the conventional commutation relations. While mathematically quite heuristic in part, local products of quantized fields do not intervene, and there are grounds for the belief that the formulation is free from nontrivial divergences.Keywords
This publication has 14 references indexed in Scilit:
- Integration and nonlinear transformations in Hilbert spaceTransactions of the American Mathematical Society, 1960
- Perturbation of continuous spectra by unbounded operators, I.Journal of the Mathematical Society of Japan, 1959
- Direct Formulation of Causality Requirements on theOperatorPhysical Review B, 1958
- Distributions in Hilbert space and canonical systems of operatorsTransactions of the American Mathematical Society, 1958
- General Relativity and the Divergence Problem in Quantum Field TheoryReviews of Modern Physics, 1957
- Tensor Algebras Over Hilbert Spaces. IIAnnals of Mathematics, 1956
- Energy corrections and persistent perturbation effects in continuous spectraPhysica, 1955
- The commutation laws of relativistic field theoryProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1952
- The S-Matrix in the Heisenberg RepresentationPhysical Review B, 1950
- Unitary representations of the Lorentz groupProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1945