Lorentz-Invariant Measure for Path Integrals in the Future Cone
We construct a measure on continuous paths in the future cone of two-dimensional space that is invariant under the orthochronous Lorentz group and quasi-invariant under the action of the diffeomorphism group. We use the proposed measure to obtain the fundamental solution of the heat equation. The result agrees with the expression obtained by other methods.
Authors
- Vladimir Viktorovich Belokurov (ORCID: https://orcid.org/0000-0001-8794-639X)
- Evgeniy T. Shavgulidze (ORCID: https://orcid.org/0000-0003-4587-2681)
- Vsevolod V. Chistiakov (ORCID: https://orcid.org/0009-0007-3101-6071)
- Klavdiia A. Lursmanashvili
Publication Details
- Journal
- arXiv (Cornell University)
- Published
- 2026-11-03
- DOI
- https://doi.org/10.48550/arxiv.2611.04669
- Primary Topic
- Mathematical and Theoretical Analysis
- Type
- preprint