17,197 research outputs found
Approximate Differential Equations for Renormalization Group Functions in Models Free of Vertex Divergencies
I introduce an approximation scheme that allows to deduce differential
equations for the renormalization group -function from a
Schwinger--Dyson equation for the propagator. This approximation is proven to
give the dominant asymptotic behavior of the perturbative solution. In the
supersymmetric Wess--Zumino model and a scalar model which do not
have divergent vertex functions, this simple Schwinger--Dyson equation for the
propagator captures the main quantum corrections.Comment: Clarification of the presentation of results. Equations and results
unchanged. Match the published version. 12 page
New mathematical structures in renormalizable quantum field theories
Computations in renormalizable perturbative quantum field theories reveal
mathematical structures which go way beyond the formal structure which is
usually taken as underlying quantum field theory. We review these new
structures and the role they can play in future developments.Comment: 26p,4figs., Invited Contribution to Annals of Physics, minor typos
correcte
From quantum electrodynamics to posets of planar binary trees
This paper is a brief mathematical excursion which starts from quantum
electrodynamics and leads to the Moebius function of the Tamari lattice of
planar binary trees, within the framework of groups of tree-expanded series.
First we recall Brouder's expansion of the photon and the electron Green's
functions on planar binary trees, before and after the renormalization. Then we
recall the structure of Connes and Kreimer's Hopf algebra of renormalization in
the context of planar binary trees, and of their dual group of tree-expanded
series. Finally we show that the Moebius function of the Tamari posets of
planar binary trees gives rise to a particular series in this group.Comment: 13 page
A Unified Elementary Approach to the Dyson, Morris, Aomoto, and Forrester Constant Term Identities
We introduce an elementary method to give unified proofs of the Dyson,
Morris, and Aomoto identities for constant terms of Laurent polynomials. These
identities can be expressed as equalities of polynomials and thus can be proved
by verifying them for sufficiently many values, usually at negative integers
where they vanish. Our method also proves some special cases of the Forrester
conjecture.Comment: 20 page
Hopf algebras in renormalization theory: Locality and Dyson-Schwinger equations from Hochschild cohomology
In this review we discuss the relevance of the Hochschild cohomology of
renormalization Hopf algebras for local quantum field theories and their
equations of motion.Comment: 29 pages, eps figures; minor changes; final versio
Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality
The Hopf algebra of undecorated rooted trees has tamed the combinatorics of
perturbative contributions, to anomalous dimensions in Yukawa theory and scalar
theory, from all nestings and chainings of a primitive self-energy
subdivergence. Here we formulate the nonperturbative problems which these
resummations approximate. For Yukawa theory, at spacetime dimension , we
obtain an integrodifferential Dyson-Schwinger equation and solve it
parametrically in terms of the complementary error function. For the scalar
theory, at , the nonperturbative problem is more severe; we transform it
to a nonlinear fourth-order differential equation. After intensive use of
symbolic computation we find an algorithm that extends both perturbation series
to 500 loops in 7 minutes. Finally, we establish the propagator-coupling
duality underlying these achievements making use of the Hopf structure of
Feynman diagrams.Comment: 20p, 2 epsf fi
Disk Partition Function and Oscillatory Rolling Tachyons
An exact cubic open string field theory rolling tachyon solution was recently
found by Kiermaier et. al. and Schnabl. This oscillatory solution has been
argued to be related by a field redefinition to the simple exponential rolling
tachyon deformation of boundary conformal theory. In the latter approach, the
disk partition function takes a simple form. Out of curiosity, we compute the
disk partition function for an oscillatory tachyon profile, and find that the
result is nevertheless almost the same.Comment: 17 pages, 2 figures. v4: discussion clarified, appendix added,
conclusions unchanged; version to appear in J.Phys.
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