{"paper":{"title":"$\\mathcal{P}\\mathcal{T}$-symmetric $-g\\varphi^4$ theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","quant-ph"],"primary_cat":"hep-th","authors_text":"Carl M. Bender, Sarben Sarkar, Wen-Yuan Ai","submitted_at":"2022-09-16T12:44:00Z","abstract_excerpt":"The scalar field theory with potential $V(\\varphi)=\\textstyle{\\frac{1}{2}} m^2\\varphi^2-\\textstyle{\\frac{1}{4}} g\\varphi^4$ ($g>0$) is ill defined as a Hermitian theory but in a non-Hermitian $\\mathcal{P}\\mathcal{T}$-symmetric framework it is well defined, and it has a positive real energy spectrum for the case of spacetime dimension $D=1$. While the methods used in the literature do not easily generalize to quantum field theory, in this paper the path-integral representation of a $\\mathcal{P}\\mathcal{T}$-symmetric $-g\\varphi^4$ theory is shown to provide a unified formulation for general $D$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.07897","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.07897/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}