996 research outputs found
The three-dimensional noncommutative Gross-Neveu model
This work is dedicated to the study of the noncommutative Gross-Neveu model.
As it is known, in the canonical Weyl-Moyal approach the model is inconsistent,
basically due to the separation of the amplitudes into planar and nonplanar
parts. We prove that if instead a coherent basis representation is used, the
model becomes renormalizable and free of the aforementioned difficulty. We also
show that, although the coherent states procedure breaks Lorentz symmetry in
odd dimensions, in the Gross-Neveu model this breaking can be kept under
control by assuming the noncommutativity parameters to be small enough. We also
make some remarks on some ordering prescriptions used in the literature.Comment: 10 pages, IOP article style; v3: revised version, accepted for
publication in J. Phys.
Supersymmetric Extension of the Snyder Algebra
We obtain a minimal supersymmetric extension of the Snyder algebra and study
its representations. The construction differs from the general approach given
in Hatsuda and Siegel ({\tt hep-th/0311002}), and does not utilize super-de
Sitter groups. The spectra of the position operators are discrete, implying a
lattice description of space, and the lattice is compatible with supersymmetry
transformations.Comment: 14 page
The Low Energy Limit of the Chern-Simons Theory Coupled to Fermions
We study the nonrelativistic limit of the theory of a quantum Chern--Simons
field minimally coupled to Dirac fermions. To get the nonrelativistic effective
Lagrangian one has to incorporate vacuum polarization and anomalous magnetic
moment effects. Besides that, an unsuspected quartic fermionic interaction may
also be induced. As a by product, the method we use to calculate loop diagrams,
separating low and high loop momenta contributions, allows to identify how a
quantum nonrelativistic theory nests in a relativistic one.Comment: 18 pages, 8 figures, Late
The coupling of fermions to the three-dimensional noncommutative model: minimal and supersymmetric extensions
We consider the coupling of fermions to the three-dimensional noncommutative
model. In the case of minimal coupling, although the infrared
behavior of the gauge sector is improved, there are dangerous (quadratic)
infrared divergences in the corrections to the two point vertex function of the
scalar field. However, using superfield techniques we prove that the
supersymmetric version of this model with ``antisymmetrized'' coupling of the
Lagrange multiplier field is renormalizable up to the first order in
. The auxiliary spinor gauge field acquires a nontrivial
(nonlocal) dynamics with a generation of Maxwell and Chern-Simons
noncommutative terms in the effective action. Up to the 1/N order all
divergences are only logarithimic so that the model is free from nonintegrable
infrared singularities.Comment: Minor corrections in the text and modifications in the list of
reference
Superfield covariant analysis of the divergence structure of noncommutative supersymmetric QED
Commutative supersymmetric Yang-Mills is known to be renormalizable for
, while finite for . However, in the
noncommutative version of the model (NCSQED) the UV/IR mechanism gives rise
to infrared divergences which may spoil the perturbative expansion. In this
work we pursue the study of the consistency of NCSQED by working
systematically within the covariant superfield formulation. In the Landau
gauge, it has already been shown for that the gauge field
two-point function is free of harmful UV/IR infrared singularities, in the
one-loop approximation. Here we show that this result holds without
restrictions on the number of allowed supersymmetries and for any arbitrary
covariant gauge. We also investigate the divergence structure of the gauge
field three-point function in the one-loop approximation. It is first proved
that the cancellation of the leading UV/IR infrared divergences is a gauge
invariant statement. Surprisingly, we have also found that there exist
subleading harmful UV/IR infrared singularities whose cancellation only takes
place in a particular covariant gauge. Thus, we conclude that these last
mentioned singularities are in the gauge sector and, therefore, do not
jeopardize the perturbative expansion and/or the renormalization of the theory.Comment: 36 pages, 11 figures. Minor correction
Canonical Quantization of the Self-Dual Model coupled to Fermions
This paper is dedicated to formulate the interaction picture dynamics of the
self-dual field minimally coupled to fermions. To make this possible, we start
by quantizing the free self-dual model by means of the Dirac bracket
quantization procedure. We obtain, as result, that the free self-dual model is
a relativistically invariant quantum field theory whose excitations are
identical to the physical (gauge invariant) excitations of the free
Maxwell-Chern-Simons theory. The model describing the interaction of the
self-dual field minimally coupled to fermions is also quantized through the
Dirac bracket quantization procedure. One of the self-dual field components is
found not to commute, at equal times, with the fermionic fields. Hence, the
formulation of the interaction picture dynamics is only possible after the
elimination of the just mentioned component. This procedure brings, in turns,
two new interaction terms, which are local in space and time while
non-renormalizable by power counting. Relativistic invariance is tested in
connection with the elastic fermion-fermion scattering amplitude. We prove that
all the non-covariant pieces in the interaction Hamiltonian are equivalent to
the covariant minimal interaction of the self-dual field with the fermions. The
high energy behavior of the self-dual field propagator corroborates that the
coupled theory is non-renormalizable. Certainly, the self-dual field minimally
coupled to fermions bears no resemblance with the renormalizable model defined
by the Maxwell-Chern-Simons field minimally coupled to fermions.Comment: 16 pages, no special macros, no corrections in the pape
Canonical Quantization of the Maxwell-Chern-Simons Theory in the Coulomb Gauge
The Maxwell-Chern-Simons theory is canonically quantized in the Coulomb gauge
by using the Dirac bracket quantization procedure. The determination of the
Coulomb gauge polarization vector turns out to be intrincate. A set of quantum
Poincar\'e densities obeying the Dirac-Schwinger algebra, and, therefore, free
of anomalies, is constructed. The peculiar analytical structure of the
polarization vector is shown to be at the root for the existence of spin of the
massive gauge quanta.The Coulomb gauge Feynman rules are used to compute the
M\"oller scattering amplitude in the lowest order of perturbation theory. The
result coincides with that obtained by using covariant Feynman rules. This
proof of equivalence is, afterwards, extended to all orders of perturbation
theory. The so called infrared safe photon propagator emerges as an effective
propagator which allows for replacing all the terms in the interaction
Hamiltonian of the Coulomb gauge by the standard field-current minimal
interaction Hamiltonian.Comment: 21 pages, typeset in REVTEX, figures not include
Nonrelativistic Quantum Particle in a Curved Space as a Constrained System
The operator and the functional formulations of the dynamics of constrained
systems are explored for determining unambiguously the quantum Hamiltonian of a
nonrelativistic particle in a curved space.Comment: 11 pages, latex, revtex, no figures. Accepted for publication in
Phys. Lett.
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