303 research outputs found

### On the quantum dynamics of non-commutative systems

This is a review paper concerned with the global consistency of the quantum
dynamics of non-commutative systems. Our point of departure is the theory of
constrained systems, since it provides a unified description of the classical
and quantum dynamics for the models under investigation. We then elaborate on
recently reported results concerned with the sufficient conditions for the
existence of the Born series and unitarity and turn, afterwards, into analyzing
the functional quantization of non-commutative systems. The compatibility
between the operator and the functional approaches is established in full
generality. The intricacies arising in connection with the explicit computation
of path integrals, for the systems under scrutiny, is illustrated by presenting
the detailed calculation of the Feynman kernel for the non-commutative two
dimensional harmonic oscillator.Comment: 19 pages, title changed, version to be published in Brazilian Journal
of Physic

### Comment on "Attractive Forces between Electrons in 2 + 1 Dimensional QED"

It is shown that a model recently proposed for numerical calculations of
bound states in QED$_3$ is in fact an improper truncation of the Aharonov-Bohm
potential.Comment: 4 page

### Nonperturbative solution of the Nonconfining Schwinger Model with a generalized regularization

Nonconfining Schwinger Model [AR] is studied with a one parameter class of
kinetic energy like regularization. It may be thought of as a generalization
over the regularization considered in [AR]. Phasespace structure has been
determined in this new situation. The mass of the gauge boson acquires a
generalized expression with the bare coupling constant and the parameters
involved in the regularization. Deconfinement scenario has become transparent
at the quark-antiquark potential level.Comment: 13 pages latex fil

### Gauge Dependence in the AdS/CFT Correspondence

We consider the AdS space formulation of the classical dynamics deriving from
the Stueckelberg Lagrangian. The on-shell action is shown to be free of
infrared singularities as the vector boson mass tends to zero. In this limit
the model becomes Maxwell theory formulated in an arbitrary covariant gauge.
Then we use the AdS/CFT correspondence to compute the two-point correlation
functions on the boundary. It is shown that the gauge dependence concentrates
on the contact terms.Comment: 13 pages, REVTEX, misprints in the abstract corrected. Minor changes.
Version to be publishe

### 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.

### 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 $Q$ turns out to be
local, gauge invariant and metric independent. Furthermore, $Q$ commutes with
all the conformal group generators. We also show that $Q$ 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.

### 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

### 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

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