179,991 research outputs found
Electromagnetic corrections in the anomaly sector
Chiral perturbation theory in the anomaly sector for is extended to
include dynamical photons, thereby allowing a complete treatment of isospin
breaking. A minimal set of independent chiral lagrangian terms is determined
and the divergence structure is worked out. There are contributions from
irreducible and also from reducible one-loop graphs, a feature of ChPT at order
larger than four. The generating functional is non-anomalous at order ,
but not necessarily at higher order in . Practical applications to
and to the amplitudes are considered. In
the latter case, a complete discussion of the corrections beyond current
algebra is presented including quark mass as well as electromagnetic effects.Comment: 26 pages, 3 figure
Maximal Sharing in the Lambda Calculus with letrec
Increasing sharing in programs is desirable to compactify the code, and to
avoid duplication of reduction work at run-time, thereby speeding up execution.
We show how a maximal degree of sharing can be obtained for programs expressed
as terms in the lambda calculus with letrec. We introduce a notion of `maximal
compactness' for lambda-letrec-terms among all terms with the same infinite
unfolding. Instead of defined purely syntactically, this notion is based on a
graph semantics. lambda-letrec-terms are interpreted as first-order term graphs
so that unfolding equivalence between terms is preserved and reflected through
bisimilarity of the term graph interpretations. Compactness of the term graphs
can then be compared via functional bisimulation.
We describe practical and efficient methods for the following two problems:
transforming a lambda-letrec-term into a maximally compact form; and deciding
whether two lambda-letrec-terms are unfolding-equivalent. The transformation of
a lambda-letrec-term into maximally compact form proceeds in three
steps:
(i) translate L into its term graph ; (ii) compute the maximally
shared form of as its bisimulation collapse ; (iii) read back a
lambda-letrec-term from the term graph with the property . This guarantees that and have the same unfolding, and that
exhibits maximal sharing.
The procedure for deciding whether two given lambda-letrec-terms and
are unfolding-equivalent computes their term graph interpretations and , and checks whether these term graphs are bisimilar.
For illustration, we also provide a readily usable implementation.Comment: 18 pages, plus 19 pages appendi
On the S-matrix renormalization in effective theories
This is the 5-th paper in the series devoted to explicit formulating of the
rules needed to manage an effective field theory of strong interactions in
S-matrix sector. We discuss the principles of constructing the meaningful
perturbation series and formulate two basic ones: uniformity and summability.
Relying on these principles one obtains the bootstrap conditions which restrict
the allowed values of the physical (observable) parameters appearing in the
extended perturbation scheme built for a given localizable effective theory.
The renormalization prescriptions needed to fix the finite parts of
counterterms in such a scheme can be divided into two subsets: minimal --
needed to fix the S-matrix, and non-minimal -- for eventual calculation of
Green functions; in this paper we consider only the minimal one. In particular,
it is shown that in theories with the amplitudes which asymptotic behavior is
governed by known Regge intercepts, the system of independent renormalization
conditions only contains those fixing the counterterm vertices with
lines, while other prescriptions are determined by self-consistency
requirements. Moreover, the prescriptions for cannot be taken
arbitrary: an infinite number of bootstrap conditions should be respected. The
concept of localizability, introduced and explained in this article, is closely
connected with the notion of resonance in the framework of perturbative QFT. We
discuss this point and, finally, compare the corner stones of our approach with
the philosophy known as ``analytic S-matrix''.Comment: 28 pages, 10 Postscript figures, REVTeX4, submitted to Phys. Rev.
Renormalization group equations for effective field theories
We derive the renormalization group equations for a generic nonrenormalizable
theory. We show that the equations allow one to derive the structure of the
leading divergences at any loop order in terms of one-loop diagrams only. In
chiral perturbation theory, e.g., this means that one can obtain the series of
leading chiral logs by calculating only one loop diagrams. We discuss also the
renormalization group equations for the subleading divergences, and the crucial
role of counterterms that vanish at the equations of motion. Finally, we show
that the renormalization group equations obtained here apply equally well also
to renormalizable theories.Comment: 40 pages, 4 figures, plain Late
Dimensional renormalization of Yukawa theories wia Wilsonian methods
In the 't Hooft-Veltman dimensional regularization scheme it is necessary to
introduce finite counterterms to satisfy chiral Ward identities. It is a
non-trivial task to evaluate these counterterms even at two loops. We suggest
the use of Wilsonian exact renormalization group techniques to reduce the
computation of these counterterms to simple master integrals. We illustrate
this method by a detailed study of a generic Yukawa model with massless
fermions at two loops.Comment: 32 pages, 9 figures, revised version: minor errors corrected, a
reference adde
Minimal surfaces in the Heisenberg group
We investigate the minimal surface problem in the three dimensional
Heisenberg group, H, equipped with its standard Carnot-Caratheodory metric.
Using a particular surface measure, we characterize minimal surfaces in terms
of a sub-elliptic partial differential equation and prove an existence result
for the Plateau problem in this setting. Further, we provide a link between our
minimal surfaces and Riemannian constant mean curvature surfaces in H equipped
with different Riemannian metrics approximating the Carnot-Caratheodory metric.
We generate a large library of examples of minimal surfaces and use these to
show that the solution to the Dirichlet problem need not be unique. Moreover,
we show that the minimal surfaces we construct are in fact X-minimal surfaces
in the sense of Garofalo and Nhieu.Comment: 26 pages, 12 figure
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