653 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
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
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
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 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
Born series and unitarity in noncommutative quantum mechanics
This paper is dedicated to present model independent results for
noncommutative quantum mechanics. We determine sufficient conditions for the
convergence of the Born series and, in the sequel, unitarity is proved in full
generality.Comment: 9 page
Noncommutative quantum mechanics: uniqueness of the functional description
The generalized Weyl transform of index is used to implement the
time-slice definition of the phase space path integral yielding the Feynman
kernel in the case of noncommutative quantum mechanics. As expected, this
representation for the Feynman kernel is not unique but labeled by the real
parameter . We succeed in proving that the -dependent
contributions disappear at the limit where the time slice goes to zero. This
proof of consistency turns out to be intricate because the Hamiltonian involves
products of noncommuting operators originating from the non-commutativity. The
antisymmetry of the matrix parameterizing the non-commutativity plays a key
role in the cancelation mechanism of the -dependent terms.Comment: 13 page
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