1,537 research outputs found
Renormalized Wick expansion for a modified PQCD
The renormalization scheme for the Wick expansion of a modified version of
the perturbative QCD introduced in previous works is discussed. Massless QCD is
considered, by implementing the usual multiplicative scaling of the gluon and
quark wave functions and vertices. However, also massive quark and gluon
counter-terms are allowed in this mass less theory since the condensates are
expected to generate masses. A natural set of expansion parameters of the
physical quantities is introduced: the coupling itself and to masses and
associated to quarks and gluons respectively. This procedure allows to
implement a dimensional transmutation effect through these new mass scales. A
general expression for the new generating functional in terms of the mass
parameters and is obtained in terms of integrals over arbitrary but
constant gluon or quark fields in each case. Further, the one loop potential,
is evaluated in more detail in the case when only the quark condensate is
retained. This lowest order result again indicates the dynamical generation of
quark condensates in the vacuum.Comment: 13 pages, one figur
Surface Waves and Forced Oscillations in QHE Planar Samples
Dispersion relations and polarizations for surface waves in infinite planar
samples in the QHE regime are explicitly determined in the small wavevector
limit in which the dielectric tensor can be considered as local. The wavelength
and frequency regions of applicability of the results extends to the infrared
region for typical experimental conditions. Then, standard samples with
millimetric sizes seem to be able to support such excitations. Forced
oscillations are also determined which should be generated in the 2DEG by
external electromagnetic sources. They show an almost frequency independent
wavevelength which decreases with the magnetic field. A qualitative model based
in these solutions is also presented to describe a recently found new class of
resonances appearing near the edge of a 2DEG in the QHE regime.Comment: latex file, 18 pages, 3 figures, spelling correcte
The Hartree-Fock state for the 2DEG at filling factor 1/2 revisited: analytic solution, dynamics and correlation energy
The CDW Hartree-Fock state at half filling and half electron per unit cell is
examined. Firstly, an exact solution in terms of Bloch-like states is
presented. Using this solution we discuss the dynamics near half filling and
show the mass to diverge logarithmically as this filling is approached. We also
show how a uniform density state may be constructed from a linear combination
of two degenerate solutions. Finally we show the second order correction to the
energy to be an order of magnitude larger than that for competing CDW solutions
with one electron per unit cell.Comment: 14 pages, no figures, extended acknowledgements, two new references
include
On Scale Invariance and Anomalies in Quantum Mechanics
We re-consider the quantum mechanics of scale invariant potentials in two
dimensions. The breaking of scale invariance by quantum effects is analyzed by
the explicit evaluation of the phase shift and the self-adjoint extension
method. We argue that the breaking of scale invariance reported in the
literature for the (r) potential, is an example of explicit and not an
anomaly or quantum mechanical symmetry breaking.Comment: 15 pp in latex, no figure
Faddeev-Jackiw approach to gauge theories and ineffective constraints
The general conditions for the applicability of the Faddeev-Jackiw approach
to gauge theories are studied. When the constraints are effective a new proof
in the Lagrangian framework of the equivalence between this method and the
Dirac approach is given. We find, however, that the two methods may give
different descriptions for the reduced phase space when ineffective constraints
are present. In some cases the Faddeev-Jackiw approach may lose some
constraints or some equations of motion. We believe that this inequivalence can
be related to the failure of the Dirac conjecture (that says that the Dirac
Hamiltonian can be enlarged to an Extended Hamiltonian including all first
class constraints, without changes in the dynamics) and we suggest that when
the Dirac conjecture fails the Faddeev-Jackiw approach fails to give the
correct dynamics. Finally we present some examples that illustrate this
inequivalence.Comment: 21 pages, Latex. To be published in Int. J. Mod. Phys.
Classical Noncommutative Electrodynamics with External Source
In a -noncommutative (NC) gauge field theory we extend the
Seiberg-Witten (SW) map to include the (gauge-invariance-violating) external
current and formulate - to the first order in the NC parameter -
gauge-covariant classical field equations. We find solutions to these equations
in the vacuum and in an external magnetic field, when the 4-current is a static
electric charge of a finite size , restricted from below by the elementary
length. We impose extra boundary conditions, which we use to rule out all
singularities, included, from the solutions. The static charge proves to
be a magnetic dipole, with its magnetic moment being inversely proportional to
its size . The external magnetic field modifies the long-range Coulomb field
and some electromagnetic form-factors. We also analyze the ambiguity in the SW
map and show that at least to the order studied here it is equivalent to the
ambiguity of adding a homogeneous solution to the current-conservation
equation
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