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At this point, we may note that the spin vector
' is always orthogonal to the world-velocity vector as
v]) momenta, and the direction of the initial neutron's spin vector
As this involves the cross product of the gradient of the density function p with the spin vector, the resulting motion is always directed perpendicularly to both quantities.
We can, however, generalize to involve a time dependent spin vector (fig.
Suppose that a spin vector in a spatial region of ordered spin vectors in the ground state with SBS happens to deviate slightly from the aligned direction of all the other spin vectors.
Because the spin vectors in the ordered region are aligned in one and the same direction, a deviation of a spin vector is corrected but is overcorrected, resulting still in a deviation, thus starting an oscillation around the aligned direction.
In a general coordinate system the spin vector in parallel obeys the equation:
micro]] are the spin vector components (here [micro], v, [lambda] = 0, 1, 2, 3).
A propagating neutron experiences a transverse rotation of its spin vector
about its momentum axis--an effect which manifestly violates parity.
mu]] are the components of the four-dimensional microscopic (micropolar) intrinsic spin vector
An axial magnetic field will rotate a transverse spin vector
about the momentum axis.