17,426 research outputs found
Superspace Formulation for the BRST Quantization of the Chiral Schwinger Model
It has recently been shown that the Field Antifield quantization of anomalous
irreducible gauge theories with closed algebra can be represented in a BRST
superspace where the quantum action at one loop order, including the Wess
Zumino term, and the anomalies show up as components of the same superfield. We
show here how the Chiral Schwinger model can be represented in this
formulation.Comment: 11 pages, Late
Irreducible pseudo 2-factor isomorphic cubic bipartite graphs
A bipartite graph is {\em pseudo 2--factor isomorphic} if all its 2--factors
have the same parity of number of circuits. In \cite{ADJLS} we proved that the
only essentially 4--edge-connected pseudo 2--factor isomorphic cubic bipartite
graph of girth 4 is , and conjectured \cite[Conjecture 3.6]{ADJLS}
that the only essentially 4--edge-connected cubic bipartite graphs are
, the Heawood graph and the Pappus graph.
There exists a characterization of symmetric configurations %{\bf
decide notation and how to use it in the rest of the paper} due to Martinetti
(1886) in which all symmetric configurations can be obtained from an
infinite set of so called {\em irreducible} configurations \cite{VM}. The list
of irreducible configurations has been completed by Boben \cite{B} in terms of
their {\em irreducible Levi graphs}.
In this paper we characterize irreducible pseudo 2--factor isomorphic cubic
bipartite graphs proving that the only pseudo 2--factor isomorphic irreducible
Levi graphs are the Heawood and Pappus graphs. Moreover, the obtained
characterization allows us to partially prove the above Conjecture
Noncommutativity and Duality through the Symplectic Embedding Formalism
This work is devoted to review the gauge embedding of either commutative and
noncommutative (NC) theories using the symplectic formalism framework. To sum
up the main features of the method, during the process of embedding, the
infinitesimal gauge generators of the gauge embedded theory are easily and
directly chosen. Among other advantages, this enables a greater control over
the final Lagrangian and brings some light on the so-called "arbitrariness
problem". This alternative embedding formalism also presents a way to obtain a
set of dynamically dual equivalent embedded Lagrangian densities which is
obtained after a finite number of steps in the iterative symplectic process,
oppositely to the result proposed using the BFFT formalism. On the other hand,
we will see precisely that the symplectic embedding formalism can be seen as an
alternative and an efficient procedure to the standard introduction of the
Moyal product in order to produce in a natural way a NC theory. In order to
construct a pedagogical explanation of the method to the nonspecialist we
exemplify the formalism showing that the massive NC U(1) theory is embedded in
a gauge theory using this alternative systematic path based on the symplectic
framework. Further, as other applications of the method, we describe exactly
how to obtain a Lagrangian description for the NC version of some systems
reproducing well known theories. Naming some of them, we use the procedure in
the Proca model, the irrotational fluid model and the noncommutative self-dual
model in order to obtain dual equivalent actions for these theories. To
illustrate the process of noncommutativity introduction we use the chiral
oscillator and the nondegenerate mechanics
Axial Anomaly from the BPHZ regularized BV master equation
A BPHZ renormalized form for the master equation of the field antifiled (or
BV) quantization has recently been proposed by De Jonghe, Paris and Troost.
This framework was shown to be very powerful in calculating gauge anomalies. We
show here that this equation can also be applied in order to calculate a global
anomaly (anomalous divergence of a classically conserved Noether current),
considering the case of QED. This way, the fundamental result about the
anomalous contribution to the Axial Ward identity in standard QED (where there
is no gauge anomaly) is reproduced in this BPHZ regularized BV framework.Comment: 10 pages, Latex, minor changes in the reference
Quantum complex scalar fields and noncommutativity
In this work we analyze complex scalar fields using a new framework where the
object of noncommutativity represents independent degrees of
freedom. In a first quantized formalism, and its canonical
momentum are seen as operators living in some Hilbert space.
This structure is compatible with the minimal canonical extension of the
Doplicher-Fredenhagen-Roberts (DFR) algebra and is invariant under an extended
Poincar\'e group of symmetry. In a second quantized formalism perspective, we
present an explicit form for the extended Poincar\'e generators and the same
algebra is generated via generalized Heisenberg relations. We also introduce a
source term and construct the general solution for the complex scalar fields
using the Green's function technique.Comment: 13 pages. Latex. Final version to appear in Physical Review
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