Speaker: Wayne Polyzou (University of Iowa)
Title: Poincar\'e invariant quantum mechanics
Abstract:
The energy scales that are studied at JLAB require a theory that is
quantum mechanical, is relativistically invariant, and can be applied
to systems of strongly interacting particles. While QCD is the
obvious theory of choice, it is difficult to apply directly to
scattering from nuclear targets in the few GeV energy range. It is
believed that QCD is an exactly Poincar\'e invariant quantum theory
that satisfies microscopic locality, cluster properties, and a
spectral condition. While microscopic locality requires that QCD is a
theory of an infinite number of degrees of freedom that is defined on
all scales, experiments probe physics in finite energy regions that
are dominated by finite numbers of degrees of freedom. Poincar\'e
invariant quantum mechanics, which is simply quantum mechanics with an
exact Poincar\'e symmetry, provides a flexible framework for
constructing realistic quantum mechanical models of systems of a
finite number of degrees freedom that are consistent with the
observable properties of QCD; Poincar\'e invariance, cluster
separability, and a spectral condition. This framework also provides
a positive solution to a long-standing problem, recently reviewed by
Schroer, concerning the existence of non-local theories satisfying
these basic axioms. I develop the formulation of the theory using
concepts that are familiar from rotational symmetry; Clebsch-Gordan
coefficients, rotation matrices, Racah coefficients, and the
Wigner-Eckart theorem, applied to the symmetry group of special
relativity. I demonstrate the flexibility of this approach by
illustrating how to construct simple models with quark confinement,
quark-string models with confinement and scattering, and a model of NN
scattering that allows pion production. Realistic few-nucleon
applications will be discussed in a subsequent seminar.