{"paper":{"title":"On the Role of the Normalization Factors $\\kappa_n$ and of the Pseudo-Metric ${\\cal P} \\neq {\\cal P}^\\dagger$ in Crypto-Hermitian Quantum Models","license":"","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Miloslav Znojil","submitted_at":"2007-10-24T11:04:42Z","abstract_excerpt":"Among ${\\cal P}$-pseudo-Hermitian Hamiltonians $H ={\\cal P}^{-1} H^\\dagger \\cal P}$ with real spectra, the ''weakly pseudo-Hermitian\" ones (i.e., those employing non-self-adjoint ${\\cal P} \\neq {\\cal P}^\\dagger$) form a remarkable subfamily. We list some reasons why it deserves a special attention. In particular we show that whenever ${\\cal P} \\neq {\\cal P}^\\dagger$, the current involutive operator of charge ${\\cal C}$ gets complemented by a nonequivalent alternative involutive quasiparity operator ${\\cal Q}$. We show how, in this language, the standard quantum mechanics is restored via the tw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.4432","kind":"arxiv","version":3},"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/0710.4432/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"}