1,049 research outputs found
Mixable Shuffles, Quasi-shuffles and Hopf Algebras
The quasi-shuffle product and mixable shuffle product are both
generalizations of the shuffle product and have both been studied quite
extensively recently. We relate these two generalizations and realize
quasi-shuffle product algebras as subalgebras of mixable shuffle product
algebras. As an application, we obtain Hopf algebra structures in free
Rota-Baxter algebras.Comment: 14 pages, no figure, references update
Exponential renormalization
Moving beyond the classical additive and multiplicative approaches, we
present an "exponential" method for perturbative renormalization. Using Dyson's
identity for Green's functions as well as the link between the Faa di Bruno
Hopf algebra and the Hopf algebras of Feynman graphs, its relation to the
composition of formal power series is analyzed. Eventually, we argue that the
new method has several attractive features and encompasses the BPHZ method. The
latter can be seen as a special case of the new procedure for renormalization
scheme maps with the Rota-Baxter property. To our best knowledge, although very
natural from group-theoretical and physical points of view, several ideas
introduced in the present paper seem to be new (besides the exponential method,
let us mention the notions of counterfactors and of order n bare coupling
constants).Comment: revised version; accepted for publication in Annales Henri Poincar
Renormalization: a quasi-shuffle approach
In recent years, the usual BPHZ algorithm for renormalization in perturbative
quantum field theory has been interpreted, after dimensional regularization, as
a Birkhoff decomposition of characters on the Hopf algebra of Feynman graphs,
with values in a Rota-Baxter algebra of amplitudes. We associate in this paper
to any such algebra a universal semi-group (different in nature from the
Connes-Marcolli "cosmical Galois group"). Its action on the physical amplitudes
associated to Feynman graphs produces the expected operations: Bogoliubov's
preparation map, extraction of divergences, renormalization. In this process a
key role is played by commutative and noncommutative quasi-shuffle bialgebras
whose universal properties are instrumental in encoding the renormalization
process
Adsorption properties and third sound propagation in superfluid He films on carbon nanotubes
We consider the adsorption properties of superfluid He films on carbon
nanotubes. One major factor in the adsorption is the surface tension force
arising from the very small diameter of the nanotubes. Calculations show that
surface tension keeps the film thickness on the tubes very thin even when the
helium vapor is increased to the saturated pressure. The weakened Van der Waals
force due to the cylindrical geometry also contributes to this. Both of these
effects act to lower the predicted velocity of third sound propagation along
the tubes. It does not appear that superfluidity will be possible on
single-walled nanotubes of diameter about one nm, since the film thickness is
less than 3 atomic layers even at saturation. Superfluidity is possible on
larger-diameter nanotube bundles and multi-walled nanotubes, however. We have
observed third sound signals on nanotube bundles of average diameter 5 nm which
are sprayed onto a Plexiglass surface, forming a network of tubes.Comment: 4 pages, accepted for Journal of Physics: Conference Series
(Proceedings of LT25
Birkhoff type decompositions and the Baker-Campbell-Hausdorff recursion
We describe a unification of several apparently unrelated factorizations
arisen from quantum field theory, vertex operator algebras, combinatorics and
numerical methods in differential equations. The unification is given by a
Birkhoff type decomposition that was obtained from the Baker-Campbell-Hausdorff
formula in our study of the Hopf algebra approach of Connes and Kreimer to
renormalization in perturbative quantum field theory. There we showed that the
Birkhoff decomposition of Connes and Kreimer can be obtained from a certain
Baker-Campbell-Hausdorff recursion formula in the presence of a Rota-Baxter
operator. We will explain how the same decomposition generalizes the
factorization of formal exponentials and uniformization for Lie algebras that
arose in vertex operator algebra and conformal field theory, and the even-odd
decomposition of combinatorial Hopf algebra characters as well as to the Lie
algebra polar decomposition as used in the context of the approximation of
matrix exponentials in ordinary differential equations.Comment: accepted for publication in Comm. in Math. Phy
Spitzer's Identity and the Algebraic Birkhoff Decomposition in pQFT
In this article we continue to explore the notion of Rota-Baxter algebras in
the context of the Hopf algebraic approach to renormalization theory in
perturbative quantum field theory. We show in very simple algebraic terms that
the solutions of the recursively defined formulae for the Birkhoff
factorization of regularized Hopf algebra characters, i.e. Feynman rules,
naturally give a non-commutative generalization of the well-known Spitzer's
identity. The underlying abstract algebraic structure is analyzed in terms of
complete filtered Rota-Baxter algebras.Comment: 19 pages, 2 figure
What is the trouble with Dyson--Schwinger equations?
We discuss similarities and differences between Green Functions in Quantum
Field Theory and polylogarithms. Both can be obtained as solutions of fixpoint
equations which originate from an underlying Hopf algebra structure. Typically,
the equation is linear for the polylog, and non-linear for Green Functions. We
argue though that the crucial difference lies not in the non-linearity of the
latter, but in the appearance of non-trivial representation theory related to
transcendental extensions of the number field which governs the linear
solution. An example is studied to illuminate this point.Comment: 5 pages contributed to the proceedings "Loops and Legs 2004", April
2004, Zinnowitz, German
Shuffle relations for regularised integrals of symbols
We prove shuffle relations which relate a product of regularised integrals of
classical symbols to regularised nested (Chen) iterated integrals, which hold
if all the symbols involved have non-vanishing residue. This is true in
particular for non-integer order symbols. In general the shuffle relations hold
up to finite parts of corrective terms arising from renormalisation on tensor
products of classical symbols, a procedure adapted from renormalisation
procedures on Feynman diagrams familiar to physicists. We relate the shuffle
relations for regularised integrals of symbols with shuffle relations for
multizeta functions adapting the above constructions to the case of symbols on
the unit circle.Comment: 40 pages,latex. Changes concern sections 4 and 5 : an error in
section 4 has been corrected, and the link between section 5 and the previous
ones has been precise
First Report of Dermestes frischii Kugelann (Coleoptera: Dermestidae) on a Human Corpse, South of Iran
The necrophagous species of beetles provide useful complementary data to estimate the post-mortem interval in forensic cases. We report, for the first time, Dermestes frischii Kugelann, 1792 larvae from a mummified human body covered with bushes and located in a canal in Sarvestan district, Fars province, south of Iran. The human corpse was a 63 year old male. The time of death was estimated to have been 23 days prior to the finding of the body based on the police investigations and confessions of a suspect. This beetle can be helpful to estimate the time of death in the future
Renormalization of gauge fields using Hopf algebras
We describe the Hopf algebraic structure of Feynman graphs for non-abelian
gauge theories, and prove compatibility of the so-called Slavnov-Taylor
identities with the coproduct. When these identities are taken into account,
the coproduct closes on the Green's functions, which thus generate a Hopf
subalgebra.Comment: 16 pages, 1 figure; uses feynmp. To appear in "Recent Developments in
Quantum Field Theory". Eds. B. Fauser, J. Tolksdorf and E. Zeidler.
Birkhauser Verlag, Basel 200
- …