Re: Massive Fermions in Four Spatial Dimensions

On May 16, 10:43 am, aasigma <acharya.anj...@xxxxxxxxx> wrote:
On May 15, 3:15 pm, Dr Tim <timrobin...@xxxxxxxxxxxxxxx> wrote:

We know that massive 1/2 spin particles in three spatial dimensions
have two spin eigenstates, known as "up" and "down".
How many eigenstates would here be if there were four spatial
dimensions?
How many in "n" spatial dimensions?

If I am not wrong,in 'n' spatial dimensions also,massive fermions have
only two spin states..'up' and 'down'.

Yes, I believe this has to do with casimir operators of the poincare
group. Massive representations of the Poincare group are determined by
the mass and the eigenvalues of the Pauli-Lubanski vector. Within a
given representation (say, spin = 1/2) the spin in the z-direction
can be used as a label for different states within the
representation.

-HD

.

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