151 research outputs found
Non-Commutative Complete Mellin Representation for Feynman Amplitudes
We extend the complete Mellin (CM) representation of Feynman amplitudes to
the non-commutative quantum field theories. This representation is a versatile
tool. It provides a quick proof of meromorphy of Feynman amplitudes in
parameters such as the dimension of space-time. In particular it paves the road
for the dimensional renormalization of these theories. This complete Mellin
representation also allows the study of asymptotic behavior under rescaling of
arbitrary subsets of external invariants of any Feynman amplitude.Comment: 14 pages, no figur
The superconducting phase transition and gauge dependence
The gauge dependence of the renormalization group functions of the
Ginzburg-Landau model is investigated. The analysis is done by means of the
Ward-Takahashi identities. After defining the local superconducting order
parameter, it is shown that its exponent is in fact gauge independent.
This happens because in the Landau gauge is the only gauge having a
physical meaning, a property not shared by the four-dimensional model where any
gauge choice is possible. The analysis is done in both the context of the
-expansion and in the fixed dimension approach. It is pointed out the
differences that arise in both of these approaches concerning the gauge
dependence.Comment: RevTex, 3 pages, no figures; accepted for publication in PRB; this
paper is a short version of cond-mat/990527
Initial States: IR and Collinear Divergences
The standard approach to the infra-red problem is to use the Bloch-Nordsieck
trick to handle soft divergences and the Lee-Nauenberg (LN) theorem for
collinear singularities. We show that this is inconsistent in the presence of
massless initial particles. Furthermore, we show that using the LN theorem with
such initial states introduces a non-convergent infinite series of diagrams at
any fixed order in perturbation theory.Comment: 4 pages, talk given at Montpellier meeting QCD'06 (to appear in the
proceedings
Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term
We consider the parametric representation of the amplitudes of Abelian models
in the so-called framework of rank Tensorial Group Field Theory. These
models are called Abelian because their fields live on . We concentrate
on the case when these models are endowed with particular kinetic terms
involving a linear power in momenta. New dimensional regularization and
renormalization schemes are introduced for particular models in this class: a
rank 3 tensor model, an infinite tower of matrix models over
, and a matrix model over . For all divergent amplitudes, we
identify a domain of meromorphicity in a strip determined by the real part of
the group dimension . From this point, the ordinary subtraction program is
applied and leads to convergent and analytic renormalized integrals.
Furthermore, we identify and study in depth the Symanzik polynomials provided
by the parametric amplitudes of generic rank Abelian models. We find that
these polynomials do not satisfy the ordinary Tutte's rules
(contraction/deletion). By scrutinizing the "face"-structure of these
polynomials, we find a generalized polynomial which turns out to be stable only
under contraction.Comment: 69 pages, 35 figure
M. Lallement. Le travail. Une sociologie contemporaine
Dans cette synthèse très complète, Michel Lallement revisite les courants de la sociologie du travail occidental, avec quelques incursions dans des disciplines voisines (philosophie, économie, histoire, psychologie, ergonomie) pour apporter sa contribution au débat sur la fin du travail. Partisan de la centralité du travail dans le fait social, l'auteur situe son analyse dans le contexte historique des sociétés industrielles, plus particulièrement depuis la seconde moitié du XXe siècle. Il s'..
Asymptotic Expansions of Feynman Amplitudes in a Generic Covariant Gauge
We show in this paper how to construct Symanzik polynomials and the Schwinger
parametric representation of Feynman amplitudes for gauge theories in an
unspecified covariant gauge. The complete Mellin representation of such
amplitudes is then established in terms of invariants (squared sums of external
momenta and squared masses). From the scaling of the invariants by a parameter
we extend for the present situation a theorem on asymptotic expansions,
previously proven for the case of scalar field theories, valid for both
ultraviolet and infrared behaviors of Feynman amplitudes.Comment: 10 pages, revtex, no figure
Critical behaviour of the compactified theory
We investigate the critical behaviour of the -component Euclidean model at leading order in -expansion. We consider it in
three situations: confined between two parallel planes a distance apart
from one another, confined to an infinitely long cylinder having a square
cross-section of area and to a cubic box of volume . Taking the mass
term in the form , we retrieve Ginzburg-Landau
models which are supposed to describe samples of a material undergoing a phase
transition, respectively in the form of a film, a wire and of a grain, whose
bulk transition temperature () is known. We obtain equations for the
critical temperature as functions of (film), (wire), (grain) and of
, and determine the limiting sizes sustaining the transition.Comment: 12 pages, no figure
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