Speaker
Prof.
Wayne Polyzou
(University of Iowa)
Description
Scattering theory can be formulated given a representation of the
quantum mechanical Hilbert space and a set of self-adjoint Poincar\'e
generators satisfying cluster properties. These are both provided by
the Osterwalder-Schrader reconstruction theorem, where the input is a
collection of Euclidean-covariant reflection-positive distributions.
In this representation both Hilbert space inner products and matrix
elements of the generators can be expressed directly in terms of
Euclidean variables, without analytic continuation. A Euclidean
version of Haag-Ruelle scattering can be formulated in this
representation, which leads to expressions for scattering observables
as strong limits. I discuss the construction of one-particle
Haag-Ruelle states in this representation and show how these states
can be used to construct wave operators. I exhibit toy model
calculations of sharp-momentum transition matrix elements over a wide
range of energies that suggest the feasibility of formulating
numerical methods to compute scattering observables in this
Euclidean representation.
Primary author
Prof.
Wayne Polyzou
(University of Iowa)
Co-authors
Dr
Gordon Aiello
(University of Iowa)
Mr
Philip Kopp
(University of Iowa)