{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T10:09:55Z","timestamp":1789034995856,"version":"build-2803163510"},"reference-count":12,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,6]],"date-time":"2026-09-06T00:00:00Z","timestamp":1788652800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The assertion that quantum states of same-type particles have to be symmetrized because they are indistinguishable has led to a debate in the foundations of quantum mechanics around topics like \u201cthisness\u201d of particles and \u201csurplus structure\u201d in spaces of quantum states. We analyze the underlying mathematical notions and find that a central issue lies in the a priori identification of n-particle Fock space with the n-fold tensor product of single-particle spaces and the corresponding failure to recognize that multi-particle quantum states are ultimately the result of actions of Hamiltonians.<\/jats:p>","DOI":"10.3390\/e28090996","type":"journal-article","created":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T17:06:58Z","timestamp":1788800818000},"page":"996","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Symmetrization and Fock Space"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9327-307X","authenticated-orcid":false,"given":"Andreas","family":"Schlatter","sequence":"first","affiliation":[{"name":"The Quantum Institute, Gloversville, NY 12078, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,6]]},"reference":[{"key":"ref_1","first-page":"185","article-title":"Exchanging Quantum Particles","volume":"1","author":"Bigaj","year":"2015","journal-title":"Philos. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Bigaj, T. (2022). Indentity and Indiscernibility in Quantum Mechanics, Palgrave-MacMillan.","DOI":"10.1007\/978-3-030-74870-8"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1086\/650211","article-title":"The Principle of the Identity of Indiscernibles and Quantum Mechanics","volume":"77","author":"Bigaj","year":"2010","journal-title":"Philos. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/s10838-020-09510-w","article-title":"Identical Quantum Particles as Distinguishable Objects","volume":"53","author":"Dieks","year":"2022","journal-title":"J. Gen. Philos. Sci.\/Z. Allg. Wiss."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1023\/A:1015439502289","article-title":"Entanglement and Properties of Composite Quantum Systems: A Conceptual and Mathematical Analysis","volume":"108","author":"Ghirardi","year":"2002","journal-title":"J. Stat. Phys."},{"key":"ref_6","first-page":"20220106","article-title":"Quantum Haecceity","volume":"381","author":"Kastner","year":"2023","journal-title":"Philos. Trans. A Math. Phys. Eng. Sci."},{"key":"ref_7","unstructured":"Teller, P. (1997). An Interpretive Introduction to Quantum Field Theory, Princeton University Press."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Kastner, R.E. (2026). The Physics behind Symmetrization. Entropy, 28.","DOI":"10.3390\/e28070777"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Friebe, C., Kuhlmann, M., Lyre, H., N\u00e4ger, P., Passon, O., and St\u00f6ckler, M. (2015). Philosophie der Quantenphysik, Springer.","DOI":"10.1007\/978-3-642-37790-7"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1103\/PhysRev.58.716","article-title":"The Connection Between Spin and Statistics","volume":"58","author":"Pauli","year":"1940","journal-title":"Phys. Rev."},{"key":"ref_11","unstructured":"Kita, T. (2025). Proof of Spins-Statistics Theorem in Quantum Mechanics of Identical Particles. arXiv."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Kastner, R.E. (2022). The Transactional Interpretation of Quantum Mechanics: A Relativistic Treatement, Cambridge University Press.","DOI":"10.1017\/9781108907538"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/9\/996\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T09:20:46Z","timestamp":1789032046000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/9\/996"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,6]]},"references-count":12,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["e28090996"],"URL":"https:\/\/doi.org\/10.3390\/e28090996","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,6]]}}}