1,412 research outputs found
Dynamics of Dollard asymptotic variables. Asymptotic fields in Coulomb scattering
Generalizing Dollard's strategy, we investigate the structure of the
scattering theory associated to any large time reference dynamics
allowing for the existence of M{\o}ller operators. We show that (for each
scattering channel) uniquely identifies, for , {\em
asymptotic dynamics} ; they are unitary {\em groups} acting on the
scattering spaces, satisfy the M{\o}ller interpolation formulas and are
interpolated by the -matrix. In view of the application to field theory
models, we extend the result to the adiabatic procedure. In the Heisenberg
picture, asymptotic variables are obtained as LSZ-like limits of Heisenberg
variables; their time evolution is induced by , which replace the
usual free asymptotic dynamics. On the asymptotic states, (for each channel)
the Hamiltonian can by written in terms of the asymptotic variables as , the generator of the
asymptotic dynamics. As an application, we obtain the asymptotic fields
in repulsive Coulomb scattering by an LSZ modified formula; in
this case, , so that are \emph{free}
canonical fields and .Comment: 34 pages, with minor improvements in the text and correction of
misprint
Gauge Invariance and Symmetry Breaking by Topology and Energy Gap
For the description of observables and states of a quantum system, it may be
convenient to use a canonical Weyl algebra of which only a subalgebra , with a non-trivial center , describes observables, the other
Weyl operators playing the role of intertwiners between inequivalent
representations of . In particular, this gives rise to a gauge
symmetry described by the action of . A distinguished case is when
the center of the observables arises from the fundamental group of the manifold
of the positions of the quantum system. Symmetries which do not commute with
the topological invariants represented by elements of are then
spontaneously broken in each irreducible representation of the observable
algebra, compatibly with an energy gap; such a breaking exhibits a mechanism
radically different from Goldstone and Higgs mechanisms. This is clearly
displayed by the quantum particle on a circle, the Bloch electron and the two
body problem.Comment: 23 page
Charge density and electric charge in quantum electrodynamics
The convergence of integrals over charge densities is discussed in relation
with the problem of electric charge and (non-local) charged states in Quantum
Electrodynamics (QED). Delicate, but physically relevant, mathematical points
like the domain dependence of local charges as quadratic forms and the time
smearing needed for strong convergence of integrals of charge densities are
analyzed. The results are applied to QED and the choice of time smearing is
shown to be crucial for the removal of vacuum polarization effects responible
for the time dependence of the charge (Swieca phenomenon). The possibility of
constructing physical charged states in the Feynman-Gupta-Bleuler gauge as
limits of local states vectors is discussed, compatibly with the vanishing of
the Gauss charge on local states. A modification by a gauge term of the Dirac
exponential factor which yields the physical Coulomb fields from the
Feynman-Gupta-Bleuler fields is shown to remove the infrared divergence of
scalar products of local and physical charged states, allowing for a
construction of physical charged fields with well defined correlation functions
with local fields
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