Spin-1/2 one- and two- particle systems in physical space without
eigen-algebra or tensor product
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.