Integral representation of covariant observables

Y. S. Kim

D.M. Healy, Franklin E. Schroeck

An orthogonality theorem is obtained for square integrable representations on homogeneous spaces of a locally compact group. From this, a series of lemmas is derived showing the informational completeness of natural covariant localization operators, as well as of the generalized Wigner distributions (matrix elements of the group). Some of these results give explicit reconstruction formulas for the quantum state from its expectation values against these families of operators. The results are applied to special (phase space) representations of the Heisenberg, affine, and Galilei groups.

K. Kraus, H -G Stark

Some quasi-free irreducible representations of the CAR algebra of a non-relativistic free Fermi field are constructed, which are covariant under certain subgroups of the extended Galilei group. The construction of fully covariant (but reducible) representations as direct integrals of partially covariant ones is described. This method is also applicable to arbitrary C*-algebras and other covariance groups.

Jukka Kiukas

N. V. Mit︠s︡kevich, В. Н. Захаров