Re: Dynamical Systems and Expansion-Contraction

>>From Osher Doctorow

The L^2(R^3) Hilbert space is actually indexed:

1) L^2_mj(R^3)

and consists of momentum wavefunctions for a particle of spin j and
mass m. The unitary representation is realized by:

2) (U(L, a)f)(p, j3) = exp(-(ipua^u)sum D(j, j'3j3)(W(L, p))f(L^(-1)p,
j'3)

where (L, A) is in P and p on the left hand side is any vector in R^3
and p on the right hand side is a scalar with p^2 = m^2 and the W(L, p)
are the Wigner rotations while the D^j matrices represent the QM
rotation subgroup in (2j + 1) dimensions, sum being over j3' where 3 is
a subscript everywhere. Also u is a subscript in pu and a superscript
in a^u.

Osher Doctorow

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