443 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
The QED(0+1) model and a possible dynamical solution of the strong CP problem
The QED(0+1) model describing a quantum mechanical particle on a circle with
minimal electromagnetic interaction and with a potential -M cos(phi - theta_M),
which mimics the massive Schwinger model, is discussed as a prototype of
mechanisms and infrared structures of gauge quantum field theories in positive
gauges. The functional integral representation displays a complex measure, with
a crucial role of the boundary conditions, and the decomposition into theta
sectors takes place already in finite volume. In the infinite volume limit, the
standard results are reproduced for M=0 (massless fermions), but one meets
substantial differences for M not = 0: for generic boundary conditions,
independently of the lagrangean angle of the topological term, the infinite
volume limit selects the sector with theta = theta_M, and provides a natural
"dynamical" solution of the strong CP problem. In comparison with previous
approaches, the strategy discussed here allows to exploit the consequences of
the theta-dependence of the free energy density, with a unique minimum at theta
= theta_M.Comment: 21 pages, Plain Te
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
Localization and symmetries
The violation of the Noether relation between symmetries and charges is
reduced to the time dependence of the charge associated to a conserved current.
For the U(1) gauge symmetry a non-perturbative control of the charge
commutators is obtained by an analysis of the Coulomb charged fields. From
this, in the unbroken case we obtain a correct expression for the electric
charge on the Coulomb states, its superselection and the presence of massless
vector bosons; in the broken case, we obtain a general non-perturbative version
of the Higgs phenomenon, i.e. the absence of massless Goldstone bosons and of
massless vector bosons. The conservation of the (gauge dependent) current
associated to the U(1) axial symmetry in QCD is shown to be compatible with the
time dependence of the corresponding charge commutators and a non-vanishing
eta' mass, as a consequence of the non locality of the (conserved) current.Comment: Invited contribution to ``The Quantum Universe'', dedicated to G.
Ghirardi for his 70th birthda
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