## Soliton-Based Approach to Axiomatic Quantization of Classical Field Theory

**Authors:** Paul J. Werbos

This paper proposes a method for the axiomatic quantization of field theories defined by a Lagrangian of the form L(ϕ, ∇ϕ, ∂tϕ) , where ϕ is a mathematical vector field typically made up of scalars, covariant vectors, tensors and so on. It reviews basic challenges in the axiomatic formulation of quantum field theory, in quantizing “soliton models” which arise in grand unification and in phenomenological nuclear physics, and unresolved issues regarding mass normalization and the radius of the electron. It proposes a new fundamental theorem (conjecture) for spectra and bound states of bosonic field theories, exploiting the Glauber-Sudarshan P representation, and suggests how this might later be extended to solve the problem of choice (ill-definedness) in the S matrix in traditional formulations of quantum theory. The Appendix provides an extension of the P representation to perform quantization into the four dimensional Fock-Hilbert space as in the formalism of Streater and Wightman, a formalism which may possibly imply dynamics which are credible but different from the canonical version of quantum field theory.

**Comments:** 11 Pages. clarifications inserted and new approach to scattering

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### Submission history

[v1] 2012-06-03 05:42:45

[v2] 2012-06-08 12:30:38

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