Antoine, Jean-Pierre
[UCL]
Moschella, U.
Coherent states for the positive mass representations of the Poincaré group in 1 + 1 dimensions have been obtained previously, using the fact that these representations are square integrable moduli of the subgroup of time translations. Here the method is extended by combining sections from the coset space into the group with homeomorphisms of the coset space (these maps are called quasi-sections). Then the generalized construction is applied to the zero mass representations of the (1 + 1)-dimensional Poincaré group, which are square integrable moduli of a subgroup of light-like translations. The resulting coherent states, indexed as before by points in phase space, yield a resolution of the identity in the Krein space of the zero mass representations (the first explicit example of such a structure), and it turns out that they coincide with the familiar wavelets based on the 'ax + b' group.
Bibliographic reference |
Antoine, Jean-Pierre ; Moschella, U.. Poincaré coherent states - The two-dimensional massless case. In: Journal of Physics A: Mathematical and General, Vol. 26, no. 3, p. 591-607 (1993) |
Permanent URL |
http://hdl.handle.net/2078.1/49878 |