61 research outputs found
Constructive field theory without tears
We propose to treat the Euclidean theory constructively in a simpler
way. Our method, based on a new kind of "loop vertex expansion", no longer
requires the painful intermediate tool of cluster and Mayer expansions.Comment: 22 pages, 10 figure
Bosonic Monocluster Expansion
We compute connected Green's functions of a Bosonic field theory with cutoffs
by means of a ``minimal'' expansion which in a single move, interpolating a
generalized propagator, performs the usual tasks of the cluster and Mayer
expansion. In this way it allows a direct construction of the infinite volume
or thermodynamic limit and it brings constructive Bosonic expansions closer to
constructive Fermionic expansions and to perturbation theory.Comment: 30 pages, 1 figur
Constructive Matrix Theory
We extend the technique of constructive expansions to compute the connected
functions of matrix models in a uniform way as the size of the matrix
increases. This provides the main missing ingredient for a non-perturbative
construction of the field theory on the Moyal four
dimensional space.Comment: 12 pages, 3 figure
EPRL/FK Group Field Theory
The purpose of this short note is to clarify the Group Field Theory vertex
and propagators corresponding to the EPRL/FK spin foam models and to detail the
subtraction of leading divergences of the model.Comment: 20 pages, 2 figure
Bosonic Colored Group Field Theory
Bosonic colored group field theory is considered. Focusing first on dimension
four, namely the colored Ooguri group field model, the main properties of
Feynman graphs are studied. This leads to a theorem on optimal perturbative
bounds of Feynman amplitudes in the "ultraspin" (large spin) limit. The results
are generalized in any dimension. Finally integrating out two colors we write a
new representation which could be useful for the constructive analysis of this
type of models
The Anderson Model as a Matrix Model
In this paper we describe a strategy to study the Anderson model of an
electron in a random potential at weak coupling by a renormalization group
analysis. There is an interesting technical analogy between this problem and
the theory of random matrices. In d=2 the random matrices which appear are
approximately of the free type well known to physicists and mathematicians, and
their asymptotic eigenvalue distribution is therefore simply Wigner's law.
However in d=3 the natural random matrices that appear have non-trivial
constraints of a geometrical origin. It would be interesting to develop a
general theory of these constrained random matrices, which presumably play an
interesting role for many non-integrable problems related to diffusion. We
present a first step in this direction, namely a rigorous bound on the tail of
the eigenvalue distribution of such objects based on large deviation and
graphical estimates. This bound allows to prove regularity and decay properties
of the averaged Green's functions and the density of states for a three
dimensional model with a thin conducting band and an energy close to the border
of the band, for sufficiently small coupling constant.Comment: 23 pages, LateX, ps file available at
http://cpth.polytechnique.fr/cpth/rivass/articles.htm
Exorcizing the Landau Ghost in Non Commutative Quantum Field Theory
We show that the simplest non commutative renormalizable field theory, the
model on four dimensional Moyal space with harmonic potential is
asymptotically safe to all orders in perturbation theor
Overview of the parametric representation of renormalizable non-commutative field theory
We review here the parametric representation of Feynman amplitudes of
renormalizable non-commutative quantum field models.Comment: 10 pages, 3 figures, to be published in "Journal of Physics:
Conference Series
Commutative limit of a renormalizable noncommutative model
Renormalizable models on Moyal space have been obtained by
modifying the commutative propagator. But these models have a divergent "naive"
commutative limit. We explain here how to obtain a coherent such commutative
limit for a recently proposed translation-invariant model. The mechanism relies
on the analysis of the uv/ir mixing in general Feynman graphs.Comment: 11 pages, 3 figures, minor misprints being correcte
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