35 research outputs found
On supermatrix models, Poisson geometry and noncommutative supersymmetric gauge theories
We construct a new supermatrix model which represents a manifestly
supersymmetric noncommutative regularisation of the
supersymmetric Schwinger model on the supersphere. Our construction is much
simpler than those already existing in the literature and it was found by using
Poisson geometry in a substantial way.Comment: 29 pages, we enlarge Section 3.3 by adding a comparison with older
results on the subject of the component expansion
The symmetries of the Dirac--Pauli equation in two and three dimensions
We calculate all symmetries of the Dirac-Pauli equation in two-dimensional
and three-dimensional Euclidean space. Further, we use our results for an
investigation of the issue of zero mode degeneracy. We construct explicitly a
class of multiple zero modes with their gauge potentials.Comment: 22 pages, Latex. Final version as published in JMP. Contains an
additional subsection (4.2) with the explicit construction of multiple zero
mode
The Origin of Chiral Anomaly and the Noncommutative Geometry
We describe the scalar and spinor fields on noncommutative sphere starting
from canonical realizations of the enveloping algebra . The gauge extension of a free spinor model, the Schwinger model on
a noncommutative sphere, is defined and the model is quantized. The
noncommutative version of the model contains only a finite number of dynamical
modes and is non-perturbatively UV-regular. An exact expresion for the chiral
anomaly is found. In the commutative limit the standard formula is recovered.Comment: 30 page
On the Renormalizability of Theories with Gauge Anomalies
We consider the detailed renormalization of two (1+1)-dimensional gauge
theories which are quantized without preserving gauge invariance: the chiral
and the "anomalous" Schwinger models. By regularizing the non-perturbative
divergences that appear in fermionic Green's functions of both models, we show
that the "tree level" photon propagator is ill-defined, thus forcing one to use
the complete photon propagator in the loop expansion of these functions. We
perform the renormalization of these divergences in both models to one loop
level, defining it in a consistent and semi-perturbative sense that we propose
in this paper.Comment: Final version, new title and abstract, introduction and conclusion
rewritten, detailed semiperturbative discussion included, references added;
to appear in International Journal of Modern Physics
Decay widths in the massive Schwinger model
By a closer inspection of the massive Schwinger model within mass
perturbation theory we find that, in addition to the -boson bound states, a
further type of hybrid bound states has to be included into the model. Further
we explicitly compute the decay widths of the three-boson bound state and of
the lightest hybrid bound state.Comment: 8 pages, Latex file, no figure
Spin Dirac Operators on the Fuzzy 2-Sphere
The spin 1/2 Dirac operator and its chirality operator on the fuzzy 2-sphere
can be constructed using the Ginsparg-Wilson(GW) algebra
[arxiv:hep-th/0511114]. This construction actually exists for any spin on
, and have continuum analogues as well on the commutative sphere
or on . This is a remarkable fact and has no known analogue in
higher dimensional Minkowski spaces. We study such operators on and the
commutative and formulate criteria for the existence of the limit from
the former to the latter. This singles out certain fuzzy versions of these
operators as the preferred Dirac operators. We then study the spin 1 Dirac
operator of this preferred type and its chirality on the fuzzy 2-sphere and
formulate its instanton sectors and their index theory. The method to
generalize this analysis to any spin is also studied in detail.Comment: 16 pages, 1 tabl
THE DYSON-SCHWINGER EQUATION FOR A MODEL WITH INSTANTONS - THE SCHWINGER MODEL
Using the exact path integral solution of the Schwinger model -- a model
where instantons are present -- the Dyson-Schwinger equation is shown to hold
by explicit computation. It turns out that the Dyson-Schwinger equation
separately holds for every instanton sector. This is due to Theta-invariance of
the Schwinger model.Comment: LATEX file 11 pages, no figure
Sum Rules for the Dirac Spectrum of the Schwinger Model
The inverse eigenvalues of the Dirac operator in the Schwinger model satisfy
the same Leutwyler-Smilga sum rules as in the case of QCD with one flavor. In
this paper we give a microscopic derivation of these sum rules in the sector of
arbitrary topological charge. We show that the sum rules can be obtained from
the clustering property of the scalar correlation functions. This argument also
holds for other theories with a mass gap and broken chiral symmetry such as QCD
with one flavor. For QCD with several flavors a modified clustering property is
derived from the low energy chiral Lagrangian. We also obtain sum rules for a
fixed external gauge field and show their relation with the bosonized version
of the Schwinger model. In the sector of topological charge the sum rules
are consistent with a shift of the Dirac spectrum away from zero by
average level spacings. This shift is also required to obtain a nonzero chiral
condensate in the massless limit. Finally, we discuss the Dirac spectrum for a
closely related two-dimensional theory for which the gauge field action is
quadratic in the the gauge fields. This theory of so called random Dirac
fermions has been discussed extensively in the context of the quantum Hall
effect and d-wave super-conductors.Comment: 41 pages, Late
The Connes-Lott program on the sphere
We describe the classical Schwinger model as a study of the projective
modules over the algebra of complex-valued functions on the sphere. On these
modules, classified by , we construct hermitian connections with
values in the universal differential envelope which leads us to the Schwinger
model on the sphere. The Connes-Lott program is then applied using the Hilbert
space of complexified inhomogeneous forms with its Atiyah-Kaehler structure. It
splits in two minimal left ideals of the Clifford algebra preserved by the
Dirac-Kaehler operator D=i(d-delta). The induced representation of the
universal differential envelope, in order to recover its differential
structure, is divided by the unwanted differential ideal and the obtained
quotient is the usual complexified de Rham exterior algebra over the sphere
with Clifford action on the "spinors" of the Hilbert space. The subsequent
steps of the Connes-Lott program allow to define a matter action, and the field
action is obtained using the Dixmier trace which reduces to the integral of the
curvature squared.Comment: 34 pages, Latex, submitted for publicatio
General bound-state structure of the massive Schwinger model
Within the Euclidean path integral and mass perturbation theory we derive,
from the Dyson-Schwinger equations of the massive Schwinger model, a general
formula that incorporates, for sufficiently small fermion mass, all the
bound-state mass poles of the massive Schwinger model. As an illustration we
perturbatively compute the masses of the three lowest bound states.Comment: 11 pages, 7 figures, needed macro: psbox.te