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PreprintCC BY 4.0arXiv

Discontinuity of Continuum Fermion Dynamics

  • Oliver Siebert
Open at sourcePDFDOICite

Abstract

We study the Heisenberg dynamics of continuum fermions in IRd interacting through a pair potential. For a large class of nonconstant pair potentials and under suitable assumptions on the dispersion relation and external potential, we prove that the dynamics fails to be pointwise-norm continuous even on the gauge-invariant CAR algebra. An automatic-continuity argument then shows that neither the CAR algebra nor its gauge-invariant subalgebra is invariant under the dynamics, with non-invariance occurring for almost all times.

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Cite

BibTeXRIS
BibTeX
@misc{siebert2026discontinuity,
  title = {{Discontinuity of Continuum Fermion Dynamics}},
  author = {Oliver Siebert},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34402},
  eprint = {2609.34402},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34402},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Discontinuity of Continuum Fermion Dynamics
AU  - Oliver Siebert
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34402
UR  - https://arxiv.org/abs/2609.34402
AB  - We study the Heisenberg dynamics of continuum fermions in IR^d interacting through a pair potential. For a large class of nonconstant pair potentials and under suitable assumptions on the dispersion relation and external potential, we prove that the dynamics fails to be pointwise-norm continuous even on the gauge-invariant CAR algebra. An automatic-continuity argument then shows that neither the CAR algebra nor its gauge-invariant subalgebra is invariant under the dynamics, with non-invariance occurring for almost all times.
ER  -