997 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.
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
Chiral Bosons Through Linear Constraints
We study in detail the quantization of a model which apparently describes
chiral bosons. The model is based on the idea that the chiral condition could
be implemented through a linear constraint. We show that the space of states is
of indefinite metric. We cure this disease by introducing ghost fields in such
a way that a BRST symmetry is generated. A quartet algebra is seen to emerge.
The quartet mechanism, then, forces all physical states, but the vacuum, to
have zero norm.Comment: 9 page
Whirling Waves and the Aharonov-Bohm Effect for Relativistic Spinning Particles
The formulation of Berry for the Aharonov-Bohm effect is generalized to the
relativistic regime. Then, the problem of finding the self-adjoint extensions
of the (2+1)-dimensional Dirac Hamiltonian, in an Aharonov-Bohm background
potential, is solved in a novel way. The same treatment also solves the problem
of finding the self-adjoint extensions of the Dirac Hamiltonian in a background
Aharonov-Casher
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
Lorentz symmetry breaking in the noncommutative Wess-Zumino model: One loop corrections
In this paper we deal with the issue of Lorentz symmetry breaking in quantum
field theories formulated in a non-commutative space-time. We show that, unlike
in some recente analysis of quantum gravity effects, supersymmetry does not
protect the theory from the large Lorentz violating effects arising from the
loop corrections. We take advantage of the non-commutative Wess-Zumino model to
illustrate this point.Comment: 9 pages, revtex4. Corrected references. Version published in PR
The Three-Dimensional Noncommutative Nonlinear Sigma Model in Superspace
We study the superspace formulation of the noncommutative nonlinear
supersymmetric O(N) invariant sigma-model in 2+1 dimensions. We prove that the
model is renormalizable to all orders of 1/N and explicitly verify that the
model is asymptotically free.Comment: 16 pages, 5 figures, Revte
Duality Symmetry in the Schwarz-Sen Model
The continuous extension of the discrete duality symmetry of the Schwarz-Sen
model is studied. The corresponding infinitesimal generator turns out to be
local, gauge invariant and metric independent. Furthermore, commutes with
all the conformal group generators. We also show that is equivalent to the
non---local duality transformation generator found in the Hamiltonian
formulation of Maxwell theory. We next consider the Batalin--Fradkin-Vilkovisky
formalism for the Maxwell theory and demonstrate that requiring a local duality
transformation lead us to the Schwarz--Sen formulation. The partition functions
are shown to be the same which implies the quantum equivalence of the two
approaches.Comment: 10 pages, latex, small changes, final version to appear in Phys. Rev.
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
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