Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-12-04
Found.Phys. 27 (1997) 305-313
Physics
High Energy Physics
High Energy Physics - Theory
8 pages. Invited contribution to Foundation of Physics for an issue honoring Prof. Lawrence Horwitz on his 65th Birthday
Scientific paper
10.1007/BF02550456
We derive an expression for the relation between two scattering transition amplitudes which reflect the same dynamics, but which differ in the description of their initial and final state vectors. In one version, the incident and scattered states are elements of a perturbative Fock space, and solve the eigenvalue problem for the `free' part of the Hamiltonian --- the part that remains after the interactions between particle excitations have been `switched off'. Alternatively, the incident and scattered states may be coherent states that are transforms of these Fock states. In earlier work, we reported on the scattering amplitudes for QED, in which a unitary transformation relates perturbative and non-perturbative sets of incident and scattered states. In this work, we generalize this earlier result to the case of transformations that are not necessarily unitary and that may not have unique inverses. We discuss the implication of this relationship for Abelian and non-Abelian gauge theories in which the `transformed', non-perturbative states implement constraints, such as Gauss's law.
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