492 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
Relativistic Quantum Mechanics and Field Theory
The problems which arise for a relativistic quantum mechanics are reviewed
and critically examined in connection with the foundations of quantum field
theory. The conflict between the quantum mechanical Hilbert space structure,
the locality property and the gauge invariance encoded in the Gauss' law is
discussed in connection with the various quantization choices for gauge fieldsComment: 33 pages, Invited talk al the Conference "Present Problems of
Theoretical Physics", Vietri April 11-16 (2003
The Gribov horizon and spontaneous BRST symmetry breaking
An equivalent formulation of the Gribov-Zwanziger theory accounting for the
gauge fixing ambiguity in the Landau gauge is presented. The resulting action
is constrained by a Slavnov-Taylor identity stemming from a nilpotent exact
BRST invariance which is spontaneously broken due to the presence of the Gribov
horizon. This spontaneous symmetry breaking can be described in a purely
algebraic way through the introduction of a pair of auxiliary fields which give
rise to a set of linearly broken Ward identities. The Goldstone sector turns
out to be decoupled. The underlying exact nilpotent BRST invariance allows to
employ BRST cohomology tools within the Gribov horizon to identify
renormalizable extensions of gauge invariant operators. Using a simple toy
model and appropriate Dirac bracket quantization, we discuss the time-evolution
invariance of the operator cohomology. We further comment on the unitarity
issue in a confining theory, and stress that BRST cohomology alone is not
sufficient to ensure unitarity, a fact, although well known, frequently
ignored.Comment: 13 pages. v2: corrected typ
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