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Representation Theory of Canonical Commutation Relations Arising from the Quantization of the Klein-Gordon Equation with an External Potential

  • Yasumichi Matsuzawa
  • Itaru Sasaki
  • Akito Suzuki
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Abstract

We investigate the Weyl representation of the canonical commutation relations for a model describing a quantized massive scalar field under the influence of an external potential. The main problem is to determine whether the Weyl representation remains equivalent to or becomes inequivalent to the original one when the mass and/or potential are changed. This problem is reduced to the study of Schrödinger operators. It turns out that the Weyl representations are inequivalent when the masses differ. Moreover, when the masses are the same, the transition between equivalence and inequivalence occurs at the decay rate −3/2 of the difference between the potentials. This contrasts with the decay rate −1 that defines the short-range condition in scattering theory.

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Cite

BibTeXRIS
BibTeX
@misc{matsuzawa2026representation,
  title = {{Representation Theory of Canonical Commutation Relations Arising from the Quantization of the Klein-Gordon Equation with an External Potential}},
  author = {Yasumichi Matsuzawa and Itaru Sasaki and Akito Suzuki},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05237},
  eprint = {2609.05237},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05237},
}
RIS
TY  - UNPB
TI  - Representation Theory of Canonical Commutation Relations Arising from the Quantization of the Klein-Gordon Equation with an External Potential
AU  - Yasumichi Matsuzawa
AU  - Itaru Sasaki
AU  - Akito Suzuki
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.05237
UR  - https://arxiv.org/abs/2609.05237
AB  - We investigate the Weyl representation of the canonical commutation relations for a model describing a quantized massive scalar field under the influence of an external potential. The main problem is to determine whether the Weyl representation remains equivalent to or becomes inequivalent to the original one when the mass and/or potential are changed. This problem is reduced to the study of Schrödinger operators. It turns out that the Weyl representations are inequivalent when the masses differ. Moreover, when the masses are the same, the transition between equivalence and inequivalence occurs at the decay rate −3/2 of the difference between the potentials. This contrasts with the decay rate −1 that defines the short-range condition in scattering theory.
ER  -