English

A modest redirection of quantum field theory solves all current problems

General Physics 2023-09-25 v3

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)\pi(x) by k(x)/ϕ(x)k(x)/\phi(x). To insure proper values for π(x)\pi(x) it is necessary to restrict 0<ϕ(x)<0<|\phi(x)|<\infty as well as 0k(x)<0\leq|k(x)|<\infty. Indeed that leads to Hamiltonian densities in which ϕ(x)p\phi(x)^p, where pp can be even integers between 44 and \infty. This leads to a completely satisfactory quantization of field theories using situations that involve scaled behavior leading to an unexpected, 2/ϕ^(x)2\hbar^2/\hat{\phi}(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.

Keywords

Cite

@article{arxiv.2308.13475,
  title  = {A modest redirection of quantum field theory solves all current problems},
  author = {John R. Klauder and Riccardo Fantoni},
  journal= {arXiv preprint arXiv:2308.13475},
  year   = {2023}
}

Comments

6 pages

R2 v1 2026-06-28T12:04:28.749Z