225 research outputs found
Constructive Field Theory in Zero Dimension
In this pedagogical note we propose to wander through five different methods
to compute the number of connected graphs of the zero-dimensional
field theory,in increasing order of sophistication. The note does not contain
any new result but may be helpful to summarize the heart of constructive
resummations, namely a replica trick and a forest formula.Comment: 12 pages,one 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
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
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