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Spin-1/2 one- and two- particle systems in physical space without eigen-algebra or tensor product
  • Sokol Andoni
Sokol Andoni
Technical University of Denmark

Corresponding Author:[email protected]

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A novel representation of spin 1/2 combines in a single geometric object the standard Pauli spin operator and spin state. Under the spin-position decoupling approximation it consists of the sum of three orthogonal vectors comprising a gauge phase. In the one-spin case the representation: (1) is Hermitian; (2) endowed with handedness; (3) yields all standard results, including the total spin angular momentum S=(√3 ℏ)⁄2; (4) relates basis spins by proper rotations, thus preserving handedness; (5) allows formalizing irreversibility in spin measurement. In the bipartite case: (1) entangled spins have precisely related gauge phases and opposite handedness; (2) maximally entangled spins relate by one of the four improper rotations in 3D: plane-reflections (triplets) and inversion (singlet); (3) the full spin expressions yield the standard total two-spin angular momentum; (4) all standard expected values for bipartite observations follow. Depending on whether spin operations act one – or two – sided, the formalism appears in two complementary forms, the ‘spinor’ or the ‘vector’ form, respectively. The proposed scheme provides a clear geometric picture of spin transformations and correlations in the 3D physical orientation space.
10 Jan 2022Submitted to Mathematical Methods in the Applied Sciences
12 Jan 2022Submission Checks Completed
12 Jan 2022Assigned to Editor
21 Jan 2022Reviewer(s) Assigned
05 Jun 2022Review(s) Completed, Editorial Evaluation Pending
06 Jun 2022Editorial Decision: Revise Major
30 Jul 20221st Revision Received
01 Aug 2022Submission Checks Completed
01 Aug 2022Assigned to Editor
01 Aug 2022Reviewer(s) Assigned
20 Oct 2022Review(s) Completed, Editorial Evaluation Pending
21 Oct 2022Editorial Decision: Revise Minor
31 Oct 20222nd Revision Received
02 Nov 2022Submission Checks Completed
02 Nov 2022Assigned to Editor
02 Nov 2022Review(s) Completed, Editorial Evaluation Pending
02 Nov 2022Reviewer(s) Assigned
03 Nov 2022Editorial Decision: Revise Minor
04 Nov 20223rd Revision Received
07 Nov 2022Assigned to Editor
07 Nov 2022Submission Checks Completed
07 Nov 2022Review(s) Completed, Editorial Evaluation Pending
07 Nov 2022Reviewer(s) Assigned
20 Nov 2022Editorial Decision: Accept