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A Modest Redirection of Quantum Field Theory Solves All Current Problems

Abstract

Standard quantization using, for example, path integration of field theory models, includes paths of momentum and field reach infinity in the Hamiltonian density, while the Hamiltonian itself remains finite. That fact causes considerable difficulties. In this paper, we represent π(x) by k(x)/ϕ(x). To insure proper values for π(x) it is necessary to restrict 0 < |ϕ(x)| < ∞ as well as 0 ≤ |k(x)| < ∞. Indeed, that leads to Hamiltonian densities in which ϕ(x)p, where p can be even integers between 4 and ∞. This leads to a completely satisfactory quantization of field theories using situations that involve scaled behavior leading to an unexpected, h2/ϕ ˆ(x)2 which arises only in the quantum aspects. Indeed, it is fair to claim that this symbol change leads to valid field theory quantizations.

Riccardo Fantoni1*, John R Klauder2

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