3,683 research outputs found
No parity anomaly in massless QED3: a BPHZL approach
In this letter we call into question the perturbatively parity breakdown at
1-loop for the massless QED_3 frequently claimed in the literature. As long as
perturbative quantum field theory is concerned, whether a parity anomaly owing
to radiative corrections exists or not will be definitely proved by using a
renormalization method independent of any regularization scheme. Such a problem
has been investigated in the framework of BPHZL renormalization method, by
adopting the Lowenstein-Zimmermann subtraction scheme. The 1-loop parity-odd
contribution to the vacuum-polarization tensor is explicitly computed in the
framework of the BPHZL renormalization method. It is shown that a Chern-Simons
term is generated at that order induced through the infrared subtractions --
which violate parity. We show then that, what is called parity anomaly, is in
fact a parity-odd counterterm needed for restauring parity.Comment: 4 pages, no figures, to appear in Physics Letters
Exact Scale Invariance of the BF-Yang-Mills Theory in Three Dimensions
The ``extended'' BF-Yang-Mills theory in 3 dimensions, which contains a
minimally coupled scalar field, is shown to be ultraviolet finite. It obeys a
trivial Callan-Symanzik equation, with all beta-functions and anomalous
dimensions vanishing. The proof is based on an anomaly-free trace identity
valid to all orders of perturbation theory.Comment: 11 pages, Late
A New Derivation of the CPT and Spin-Statistics Theorems in Non-Commutative Field Theories
We propose an alternative axiomatic description for non-commutative field
theories (NCFT) based on some ideas by Soloviev to nonlocal quantum fields. The
local commutativity axiom is replaced by the weaker condition that the fields
commute at sufficiently large spatial separations, called asymptotic
commutativity, formulated in terms of the theory of analytic functionals. The
question of a possible violation of the CPT and Spin-Statistics theorems caused
by nonlocality of the commutation relations
is investigated. In spite of this
inherent nonlocality, we show that the modification aforementioned is
sufficient to ensure the validity of these theorems for NCFT. We restrict
ourselves to the simplest model of a scalar field in the case of only
space-space non-commutativity.Comment: The title is new, and the analysis in the manuscript has been made
more precise. This revised version is to be published in J.Math.Phy
Global stabilization of fixed points using predictive control
We analyze the global stability properties of some methods of predictive control. We particularly focus on the optimal control function introduced by de Sousa Vieira and Lichtenberg [Phys. Rev. E54, 1200 (1996)]. We rigorously prove that it is possible to use this method for the global stabilization of a discrete system xn+1=f(xn) into a positive equilibrium for a class of maps commonly used in population dynamics. Moreover, the controlledsystem is globally stable for all values of the control parameter for which it is locally asymptotically stable. Our study highlights the difficulty of obtaining global stability results for other methods of predictive control, where higher iterations of f are used in the control scheme.Ministerio de Ciencia e InnovaciónFondo Europeo de Desarrollo Regiona
Supersymmetric Field-Theoretic Models on a Supermanifold
We propose the extension of some structural aspects that have successfully
been applied in the development of the theory of quantum fields propagating on
a general spacetime manifold so as to include superfield models on a
supermanifold. We only deal with the limited class of supermanifolds which
admit the existence of a smooth body manifold structure. Our considerations are
based on the Catenacci-Reina-Teofillatto-Bryant approach to supermanifolds. In
particular, we show that the class of supermanifolds constructed by
Bonora-Pasti-Tonin satisfies the criterions which guarantee that a
supermanifold admits a Hausdorff body manifold. This construction is the
closest to the physicist's intuitive view of superspace as a manifold with some
anticommuting coordinates, where the odd sector is topologically trivial. The
paper also contains a new construction of superdistributions and useful results
on the wavefront set of such objects. Moreover, a generalization of the
spectral condition is formulated using the notion of the wavefront set of
superdistributions, which is equivalent to the requirement that all of the
component fields satisfy, on the body manifold, a microlocal spectral condition
proposed by Brunetti-Fredenhagen-K\"ohler.Comment: Final version to appear in J.Math.Phy
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