Speaker
Description
The inability to distinguish inertial coordinate systems by measuring
quantum observables implies that equivalent states in different
inertial coordinate systems are related by a unitary representation of
the Poincar\'e group on the Hilbert space of the quantum theory.
These representations can be decomposed into a direct integral of
irreducible representations. This decomposition is relevant for both
interacting and non-interacting theories. Poincar\'e covariant,
Lorentz covariant and Euclidean covariant treatments of irreducible
representations are distinguished by different representations of the
Hilbert space. The different Hilbert space representations are in
terms of square integrable functions of the eigenvalues of commuting
observables, representations with Lorentz covariant kernels (Wightman
functions) and representations with reflection-positive Euclidean
covariant kernels. The relation between these representations is
developed by starting with the representations in terms of square
integrable functions of the eigenvalues of commuting observables. The
treatment of the dynamics in each representation is discussed.
