# spin space

## spin space

[′spin ‚spās]
(mathematics)
The two-dimensional vector space over the complex numbers, whose unitary unimodular transformations are a two-dimensional double-valued representation of the three-dimensional rotation group; its vectors can represent the various spin states of a particle with spin ½, and its unitary unimodular transformations can represent rotations of this particle.
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References in periodicals archive ?
v = [+ or -]1 designates the value index for [K.sup.[+ or -]], [[tau].sub.x,y,z] and [[sigma].sub.x,y,z] are Pauli matrices in lattice space and spin space, respectively.
Throughout the text, a hat means a 2x2 matrix in spin space and [alpha], [beta] = [up arrow], [down arrow].
Further, [bar.b](n) is a real vector in the spin space, normalizable by condition
For spin-triplet pairing, the order parameter [??][equivalent to] [D.sub.[alpha][beta]] (n) is a symmetric matrix in the spin space, which near the Fermi surface can be written as follows (see, e.g., ):
In reality, according to (2) and (3), the nonrelativistic ordinary vector vertex is represented by its temporal component; that is, it is a scalar matrix in spin space. The ordinary axial-vector vertices of a particle and a hole are represented by space-vectors whose components consist of spin matrices.
and three-dimensional spin space [R.sup.3] = {[S.sub.i]} with the coordinates [S.sub.i].
Vector model of spinning particle with SO(2,3) covariant spin space has been constructed in .
Exploiting this equivalence there is in principle no difference between manipulations in the spin space of neutrons with the orthogonal basis {|[up arrow]>, |[down arrow]>} as eigenstates of [[sigma].sub.z], and momentum space with {|k>, |k'>} as orthogonal basis vectors corresponding to two directions of the neutron beam in an interferometer.
Experience the exciting new twist and spin Space Orbiters - whirling vehicles equipped with the very latest `zap guns'.

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