2014/11/30 by K. B. Wharton, K B Wharton, D. Koch +1 · 1 citation
Mathematics · Physics and Astronomy · Social Sciences · #Algebraic and Geometric Analysis #Bloch sphere #International Science and Diplomacy #Order (exchange) #Perspective (graphical) #Quantum and Classical Electrodynamics #Quaternion #Representation (politics) #Space (punctuation) #Spinor #Unit (ring theory) #Unit sphere #Unit vector #msc:20G45 #quant-ph
paper · pdf · doi:10.1088/1751-8113/48/23/235302
published as J. Phys. A: Math. Theor. 48 (2015) 235302 · 25 pages, 1 figure; Referee-inspired improvements; accepted for publication in J. Phys. A
arxiv created 2015/04/23 · openalex publication_date 2015/05/19 · arxiv updated 2015/06/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The spinor representation of spin-1/2 states can equally well be mapped to a single unit quaternion, yielding a new perspective despite the equivalent mathematics. This paper first demonstrates a useable map that allows Bloch-sphere rotations to be represented as quaternionic multiplications, simplifying the form of the dynamical equations. Left-multiplications generally correspond to non-unitary transformations, providing a simpler (essentially classical) analysis of time-reversal. But the quaternion viewpoint also reveals a surprisingly large broken symmetry, as well as a potential way to restore it, via a natural expansion of the state space that has parallels to second order fermions. This expansion to ‘second order qubits’ would imply either a larger gauge freedom or a natural space of hidden variables.