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We find that, in analogy to the Kerr-Newman-AdS Dirac Hamiltonian in $(1+3)$ dimensions, essential self-adjointness on $C_0^{\\infty}(r_+,\\infty)^2$ of the reduced (radial) Hamiltonian is implemented only if a suitable relation between the mass $\\mu$ of the Dirac field and the cosmological radius $l$ holds true. The very presence of a boundary-like behaviour of $r=\\infty$ is at the root of this problem. Also, we determine i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1007.4439","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-26T12:42:29Z","cross_cats_sorted":["gr-qc","math.MP"],"title_canon_sha256":"38e0fae50ad46ee5cc4c3f37c7000350444b75ac5581f86448c5a6b9e9d0f43e","abstract_canon_sha256":"c1c851bb5e390833f490e666ebdeace2641d6b6a8421ddd86d6f1535a45a6911"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:07.117104Z","signature_b64":"qqTU1ztQcTEwhBbPtWGbshp4vjrk4xrq3HnsyAXXp6x+hkyqulTvxJoCGO/04BSoLuKO9pVDBqkaiwrxESvVCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4fa6de536881a66da183cc2e23166d4197542d360914cc6f1e801def304ad5d","last_reissued_at":"2026-05-18T04:33:07.116464Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:07.116464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum properties of the Dirac field on BTZ black hole backgrounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math.MP"],"primary_cat":"math-ph","authors_text":"Francesco Belgiorno, Francesco Dalla Piazza, Oliver F Piattella, Sergio L Cacciatori","submitted_at":"2010-07-26T12:42:29Z","abstract_excerpt":"We consider a Dirac field on a $(1 + 2)$-dimensional uncharged BTZ black hole background. 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