Quantum ${{\mathbb{F}}_{{\rm un}}}$: the q = 1 limit of Galois field quantum mechanics, projective geometry and the field with one element

Chang, Lay Nam; Lewis, Zachary; Minic, Djordje; Takeuchi, Tatsu

doi:10.1088/1751-8113/47/40/405304

Quantum $${{\mathbb{F}}_{{\rm un}}}$$: the q = 1 limit of Galois field quantum mechanics, projective geometry and the field with one element

Journal Article · Tue Sep 23 00:00:00 EDT 2014 · Journal of Physics. A, Mathematical and Theoretical

DOI:https://doi.org/10.1088/1751-8113/47/40/405304· OSTI ID:1594440

Chang, Lay Nam ^[1]; Lewis, Zachary ^[2]; Minic, Djordje ^[2]; Takeuchi, Tatsu ^[3]

Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); Virginia Polytechnic Institute and State University
Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); Univ. of Tokyo (Japan)

We argue here that the q = 1 limit of Galois field quantum mechanics, which was constructed on a vector space over the Galois field $${{\mathbb{F}}_{q}}=GF(q)$$, corresponds to its 'classical limit', where superposition of states is disallowed. Furthermore, the limit preserves the projective geometry nature of the state space, and can be understood as being constructed on an appropriately defined analogue of a 'vector' space over the 'field with one element' $${{\mathbb{F}}_{1}}$$.

View Accepted Manuscript (DOE)

Research Organization:: Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

Grant/Contract Number:: SC0009973

OSTI ID:: 1594440

Alternate ID(s):: OSTI ID: 22332440

Journal Information:: Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 40 Vol. 47; ISSN 1751-8113

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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Quantum $${{\mathbb{F}}_{{\rm un}}}$$: the q = 1 limit of Galois field quantum mechanics, projective geometry and the field with one element

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