10 research outputs found
Maximally Symmetric Spin-Two Bitensors on and
The transverse traceless spin-two tensor harmonics on and may be
denoted by . The index labels the (degenerate) eigenvalues
of the Laplacian and the other indices. We compute the bitensor
where are distinct
points on a sphere or hyperboloid of unit radius. These quantities may be used
to find the correlation function of a stochastic background of gravitational
waves in spatially open or closed Friedman-Robertson-Walker cosmologies.Comment: 12 pages, RevTeX, uuencoded compressed .tex file, minor typos
correcte
Field on Poincare group and quantum description of orientable objects
We propose an approach to the quantum-mechanical description of relativistic
orientable objects. It generalizes Wigner's ideas concerning the treatment of
nonrelativistic orientable objects (in particular, a nonrelativistic rotator)
with the help of two reference frames (space-fixed and body-fixed). A technical
realization of this generalization (for instance, in 3+1 dimensions) amounts to
introducing wave functions that depend on elements of the Poincare group . A
complete set of transformations that test the symmetries of an orientable
object and of the embedding space belongs to the group . All
such transformations can be studied by considering a generalized regular
representation of in the space of scalar functions on the group, ,
that depend on the Minkowski space points as well as on the
orientation variables given by the elements of a matrix .
In particular, the field is a generating function of usual spin-tensor
multicomponent fields. In the theory under consideration, there are four
different types of spinors, and an orientable object is characterized by ten
quantum numbers. We study the corresponding relativistic wave equations and
their symmetry properties.Comment: 46 page
An elementary approach to 6j-symbols (classical, quantum, rational, trigonometric, and elliptic)
Elliptic 6j-symbols first appeared in connection with solvable models of statistical mechanics. They include many interesting limit cases, such as quantum 6j-symbols (or q-Racah polynomials) and Wilsonâs biorthogonal 10W9 functions. We give an elementary construction of elliptic 6j-symbols, which immediately implies several of their main properties. As a consequence, we obtain a new algebraic interpretation of elliptic 6j-symbols in terms of Sklyanin algebra representations