Skip to content
DraconiticResearch
Search Sources API
190,332 studies31 sourcesUpdated 42 min ago
PreprintarXiv licencearXiv

Supersymmetric quantum mechanics on a Kähler space

  • Olaf Lechtenfeld
  • Fin Müller
Open at sourcePDFDOICite

Abstract

We prove that the classical part of the Nicolai map for a supersymmetric free nonrelativistic particle moving on a Kähler manifold is linear in the Kähler metric and local for its velocity. Moreover, we give an exact expression for the one-loop correction of the map in terms of the Kähler potential and point out a direct way to higher loop order. This provides another example for the rare cases of exact Nicolai maps, and the first all-order one-loop result. As a check we have verified the Nicolai-map conditions to zero and one-loop order (free-action and determinant-matching). A graphical representation is given as well.

Related

  1. Scattering, bound states, and resonances in the one-dimensional Dirac equation via supersymmetric quantum mechanics
    Camila C. Soares, Luis B. Castro, Antonio S. de Castro
    arXivPreprintarXiv licenceFull textMathematical physicsHigh-energy & particle physicsarXiv
  2. Spatial degeneracy along weak geodesics in the space of Kähler potentials
    Xia Xiao, Qi Yao
    arXivPreprintarXiv licenceFull textAnalysis & PDEsGeometry & topologyarXiv
  3. Hamiltonian dynamics with nonconservative forces on extended phase space: An analytical mechanics derivation
    Joseph T. A Peterson, Manoranjan Majji, John L. Junkins
    arXivPreprintCC BY 4.0Full textGeometry & topologyMathematical physicsarXiv
  4. Quantum supersymmetric pairs and the Serre relations via iHopf algebras
    Jiayi Chen, Shiquan Ruan, Hongying Zhu
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Quantum Elliptic Cohomology From Four-Dimensional Minimal Supersymmetric Gauge Theories
    Ilka Brunner, Peng Cheng, Hans Jockers
    arXivPreprintCC BY-NC-SA 4.0Full textAlgebra & number theoryMathematical physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{lechtenfeld2026supersymmetric,
  title = {{Supersymmetric quantum mechanics on a Kähler space}},
  author = {Olaf Lechtenfeld and Fin Müller},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.00476},
  eprint = {2610.00476},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.00476},
}
RIS
TY  - UNPB
TI  - Supersymmetric quantum mechanics on a Kähler space
AU  - Olaf Lechtenfeld
AU  - Fin Müller
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.00476
UR  - https://arxiv.org/abs/2610.00476
AB  - We prove that the classical part of the Nicolai map for a supersymmetric free nonrelativistic particle moving on a Kähler manifold is linear in the Kähler metric and local for its velocity. Moreover, we give an exact expression for the one-loop correction of the map in terms of the Kähler potential and point out a direct way to higher loop order. This provides another example for the rare cases of exact Nicolai maps, and the first all-order one-loop result. As a check we have verified the Nicolai-map conditions to zero and one-loop order (free-action and determinant-matching). A graphical representation is given as well.
ER  -