Physics Reports vol.154

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To re-interpret this Wigner ket as a "Minkowski ket" with the intrinsic labels (s,m s) we see that we must "align the bosons" by using the boost operator Bp, in spin space only (generators defined by eq. 17)). 5) Next we observe that a boost transformation is actually a function only of the three variables p--and hence independent of the mass (=length of the four vector). P)-½P we can define the operator U(B~) on an arbitrary ket. 1) in the form: U(O,A) U(B~I) spin I p(s); Sms>^ = m~'sU(Bp1)Spin ] p' (s); Sm's> , D m s , m s (Bp I ABp).

It result is independent of the mass M(s), intrinsic is useful to observe that this and that the spin We can now factorize the m a t r i x element in eq. result is: (s,m s) are spin labels. 2). The 50 m' s i~ ABp) I P' (S) ;sin's > P' = U(A) I p(S);sm s> Ds , (Bp_ ms'ms Before we can use this result in eq. 1), we must properly re-interpret the Wigner kets that appear in this equation. The Wigner ket ]p(s) ; sm > is the direct product of the spatial ket ]P'P0 = [~2+ M2(s)]½> s with the spin ket IS,ms> whose labels are defined by the action of the generators Sij in eq.

We also discuss into a single theorems structure of this M i n k o w s k i Generalities. covariant trajectory. space 3, This point the c o n s i s t e n c y equally clear that the states many unitary symmetry is intimately the coordinates (X,t) least spin-½ W i a n e r incapable the COOP DINATES Thomas in o b t a i n i n g advantage form a relation satisfactory of features simply b e i n a and d e m o n s t r a t e s concents. 'composite Moreover, it is are all object' and the s t r u c t u r e of m u s t be improved.

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