i knew was going on a road to destruction when i tried this: you know how
you can derive the explicit forms of pauli matrices by requiering that:
sigma(3) = 1 0
0 -1
and using the commutation relations between them (and all of the other
properties, im not sure if that is even necessary)
so, in the same way i tried to derive dirac matrices alpha(i), by
considering the standard representation (dirac's) for beta. and i've used
all of the properties which are known to me (standard stuff from, say
Greiner: Relativistic Quantum Mechanics), and yet came to nothing. i mean
not nothing: i've bringed down the number of unknown parameters down to 4
(starts with 16), BUT I CANT GET ANY FURTHER !!!
i know, i know, it is the stupidist thing to do - no one does that stuff;
you first write the matrices, and check out if they satisfy all the
necessary properties, but unfortunately it's too late now. i wanted to do
this cause it seemed more like a mathematicians approach, but now i'm stuck,
and embarassed on how much time i spent working on this generally irrelevant
problem...anyway, this apathy is lasting for days now, and this post is my
last chance; SO IF ANYONE KNOWS HOW TO DO THIS, OR WHERE TO READ HOW TO DO
THIS IN THE WAY I SUGGESTED I BEGG THEM TO REPLY TO THIS POST...
dont laugh...well not to much:)...help me!
.
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